In Shemoneh Esrei of Aseres Yimei Teshuvah the tenth blessing of Hashiva Shofteinu concludes with the words “Hamelech Hamishpat” in place of “Melech Ohave Tzedaka Umishpat”. [This emphasizes that Hashem is the King that is currently in judgment at this time.]
Forgot to say Hamelech Hamishpat: If one did not conclude with ‘Hamelech Hamishpat’, or is in doubt as to how he concluded, then if he already began the next blessing, he is to continue Shemoneh Esrei and is not to go back to the blessing of Hashiva. In such a case it is proper to repeat Shemoneh Esrei [from the beginning] as a Toras Nedava after he concludes his prayers. There is no need to novelize anything in one’s Nedava prayer as is always the rule upon repeating a prayer due to doubt.
Remembered prior to beginning the next blessing: If he remembered prior to beginning the next blessing, then if the amount of time to say “Shalom Alecha Rebbe” has not passed since he concluded the blessing, he is to correct himself and say “Hamelech Hamishpat”. He is then to continue regularly from there. If however this amount of time has already passed, then he is not to correct himself and is rather to continue Shemoneh Esrei as usual. After he concludes his Shemoneh Esrei it is proper to repeat Shemoneh Esrei as a Toras Nidava as stated above.
Hamelech Hakodesh and Hamelech Hamishpat versus Melech Hakadosh and Melech Hamishpat:
One must recite Hamelech Hakadosh and Hamelech Hamishpat with the letter Hei. If one did not do so then some Poskim rule one does not fulfill his obligation. However most Poskim conclude one does fulfill his obligation and so is the final ruling.
What is the law if one recited Hamelech Hakadosh or Hamelech Hamishpat in Shemoneh Esrei after Aseres Yimei Teshuvah?
One who recited Hamelech Hakadosh or Hamelech Hamishpat during Shemoneh Esrei of after Aseres Yimei Teshuvah, fulfills his obligation and is not required to repeat Shemoneh Esrei.
Zachreinu; Mi Chamocha; Ukesov; Ubisefer:
The Geonim instituted that throughout Aseres Yimei Teshuvah one is to add the following prayers: Zachreinu Lechayim in the blessing of Avos [1st blessing], Mi Chamocha in the blessing of Gevuros [2nd blessing], Ukesov in the blessing of Hodaah [2nd to last blessing], and Ubisefer in the blessing of Sim Shalom.
Forgot to recite: If one forgot to say any of the above additions, then if he already said Hashem’s name in that closing blessing, such as he said Baruch Ata Hashem in “Mechayeh Hameisim”, then he is to continue with the prayer. If one remembered to say it prior to saying Hashem’s name in the concluding blessing [even if he already said Baruch Ata, but not Hashem], he is to say it in the area that he remembers and then continue from where he left off. [In such a case some Poskim rule that one is to say the omitted part at the conclusion of the Amidah after saying the second Yehi Ratzon.]
Bowing by Zachreinu and Mi Chamocha: Some have the custom to bow in Shemoneh Esrei of Rosh Hashanah and Yom Kippur upon reciting the words Zachreinu and Mi Chamocha. See Halacha 6A!
Repeating the words Ukesov and Ubesefer during the Chazan’s repetition:
When the Chazon repeats Shemoneh Esrei, the Chabad custom is that the congregation recites aloud the verses of Ukesov and Ubisefer but not Zachreinu or Mi Chamocha. This applies equally on Shabbos and Yom Tov.
Sparks of Kabala
The stanza of Zachreinu contains exactly eleven words. These eleven words correspond to the eleven Sefiros beginning from Keser. It contains 48 letters corresponding to the names “Eh-yeh Havaya” with the Kolel.
Upon reciting the words “Melech Chafeitz Bachaim” one is to intend to draw eternal life to our souls. Upon reciting “Vekasveinu Bisefer Hachaim” one is to intend to draw a good and long life to our bodies.
Mi Chamocha & Gilgul Neshamos:
On the day of Rosh Hashanah all the souls which require reincarnation into this world [i.e. Gilgul] are judged. This is why the dialect Mi Chamocha, which is added during Aseres Yimei Teshuvah, contains the words “Zocher Leyitzurav Berachamim Lechaim” [remember your creations with mercy for life] and not “Zocher Osanu” or “Zachreinu” [remember us] as is said by the other added stanzas. The reason is because it includes a request of mercy for the souls that will be returned to bodies in this world. It is also for this reason that this stanza was added in the blessing of Techiyas Hameisim [Mechayeh Meisim-resurrection], as it hints to the future life of the souls requiring a Gilgul.
 Admur 582/2
 Admur ibid; Taz 582/1
There is a dispute in Rishonim and Poskim regarding if omitting Hamelech Hamishpat requires the repetition of Shemoneh Esrei. Admur ibid records both opinions and states as follows: Some opinions [Rama 118/1] rule that one does not need to repeat Shemoneh Esrei if he mistakenly said Melech Oheiv. The reason for this is because in these words as well the term king/Melech is mentioned. Other opinions [Michaber 582/1; Rif Rambam] however rules one must return to the blessing of Hashiva and say the proper conclusion of Hamelech Hamishpat, and if he has already concluded Shemoneh Esrei he must repeat Shemoneh Esrei from the beginning. Their reasoning is because the normal wording emphasizes Tzedakah more than Mishpat and during Aseres Yimei Teshuvah one is required to mention and focus on Mishpat and not Tzedakah. Practically Admur concludes “Safek Brachos Lihakel” and therefore we do not return to the blessing of Hashiva Shofteinu. Nevertheless, after concluding Shemoneh Esrei one is to pray again as a Tefilas Nedava. [Admur ibid; and so concludes Taz ibid]
Other Opinions: Some Poskim rule one does not fulfill his obligation and must thus repeat Shemoneh Esrei. [Michaber 582/1; Beis Yosef 582; Rif; Rambam; Rosh; Tosafus; Levush; Peri Chadash 582/1; Birkeiy Yosef 118/2; 582/1; Mamar Mordechai 118/2; Shalmei Tzibur 312] Others rule that one fulfills his obligation and there is no need at all to repeat Shemoneh Esrei even as a Nedava. [Rama 118/1; Darkei Moshe 582/3; Ravaya; Reb Yechiel [brother of Tur]; Hagahos Maimanis; Rashba; Bach; M”A 582/1; Mateh Moshe; Shlah] Practically the Poskim conclude that Safek Brachos Lihakel and one is thus not to repeat Shemoneh Esrei. [Kneses Hagedola 582/2; Elya Raba 582/5; Admur ibid; Chayeh Adam 24/16; Kitzur SHU”A 129/3; Ben Ish Chaiy Netzavim 19; Derech Hachaim 2; M”B 118/3; 582/6; Kaf Hachaim 118/2 and 582/8]
Ruling of Sefaradim: Some Sefaradi Poskim rule that although according to the Michaber one must return to that blessing or repeat Shemoneh Esrei, nevertheless in this instance that there are so many Poskim that argue we apply the rule of Safek Brachos Lihakel even against the ruling of the Michaber. Hence even those of Sefaradic Jewry do not repeat Shemoneh Esrei. [Ben Ish Chaiy Netzavim 19; Kaf Hachaim 118/2] Others however rule that the majority of Sefaradi Poskim agree with the Michaber and hence the Sefaradim are to follow his ruling and return to Hashiva or repeat Shemoneh Esrei. This applies even during the Chazan’s repetition. [Yabia Omer 2/10; 7/51; Piskeiy Teshuvos 582/1]
 Implication in Admur ibid; 107/2
The reason: One cannot repeat the prayer as a Nedava only from the blessing of Hashiva, having it combine with the first half which was valid, as one cannot have the prayer be partially a Nedava and partially an obligation, just like a Karban cannot be half of each. Thus if in if in truth we rule that his first Shemoneh Esrei was valid it ends up that his current blessings from Hashiva are in vain and not a valid Nedava. [107/2]
Other Opinions: Some Poskim rule that one is to only repeat from Hashiva as a Nedava. [Rav Medini in Or Li 30] The Poskim however negate his opinion based on the above. [Yabia Omer 2/10]
 Admur ibid; Taz 582/1
The reason: As according to the second opinion he has not fulfilled his obligation. [ibid]
Other opinions: Some Poskim rule that one is not to repeat the prayer as a Nedava being that a Nedava requires a lot of concentration. [Kaf Hachaim 118/2]
 Admur ibid and 107/1
 Shaar Hakavanos; Elya Raba 582/5; M”B 118/2 in name of Derech Hachaim; Kaf Hachaim 118/2; Admur ibid writes the Hei
 Opinion brought in Elya Raba ibid [regarding Hamelech Hamishpat]; Opinions brought in M”B ibid; Shalmei Tzibur 315; see Kaf Hachaim 118/2
 Peri Chadash 582/1; Machazik Bracha 582/1; P”M 118 M”Z 2; Derech Hachaim 1; M”B 118/2; Zechor Leavraham 118/2; Piskeiy Teshuvos 582/5
 Olas Tamid 118/2; Bach 582; Kneses Hagedola 108/6; Elya Raba 108-end; Peri Chadash 582/1; Mateh Yehuda; Beir Heiytiv 108/1; Birkeiy Yosef 118/3; Machazik Bracha 582/2; P”M 118 A”A 1; Beis Oved 118/5; Shaareiy Teshuvah 108/1 [that so is the ruling of most Achronim]; Derech Hachaim 33/46 and 72; Kitzur SHU”A 129/3; Mishneh Berurah 108/1; Ketzos Hashulchan 21/4; Kaf Hachaim 118/3
Other Poskim: Some Poskim rule one is required to repeat Shemoneh Esrei. [Rame in Alfasi Zuta end of Brachos, brought in Machazik Bracha ibid] Other Poskim conclude that it is best to repeat Shemoneh Esrei as a Toras Nedava. [Mamar Mordechai 118/2; Shalmei Tzibur 122; Beir Heiytiv ibid in his understanding of Taz 582/2; Peri Chadash ibid concludes if one repeats Shemoneh Esrei as a Nedava he is blessed. See Shaareiy Teshuvah ibid]
Opinion of Taz: The Beir Heiytiv ibid learns that according to the Taz 582/2 which rules one must repeat Betoras Nedava during Aseres Yimei Teshuvah if he said the wrong Nusach in Hamelech Hamishpat, similarly if one made a mistake during the rest of the year he is to repeat the prayer as a Nedava. However the Shaareiy Teshuvah ibid negates this suggestion saying the Taz was only stringent by Aseres Yimei Teshuvah when we want to fulfill our obligation according to all.
Opinion of Admur: Admur 582/2 rules like the Taz in 582/2 that during Aseres Yimei Teshuvah one is to repeat the prayer as a Nedava. Thus there is room to learn in his opinion as learns the Beir Heiytiv ibid, that also during the year if the wrong Nussach was recited one is to repeat the prayer as a Toras Nedava. Practically however the Ketzos Hashulchan ibid rules it is not to be recited and that so is implied from Admur 108/18 that only when one has stated a lie must the prayer be repeated. Likewise the Nesiv Hachaim, which wrote glosses on the Derech Hachaim according to the opinion Admur, does not record any dissenting opinion of Admur in the above. Hiskashrus Yom Kippur likewise writes one is not required to repeat Shemoneh Esrei.
 Correct pronunciation of Zachreinu and Kasveinu: The word Zachreinu and Kasveinu is stated with a Kamatz under the Zayin [Zachrein; Kasveinu] as this is the form of a request from G-d. It is not stated with a Cholam-Zochreinu/Kosveinu- as this is a mere statement that G-d is our remembrance and not a request. [Levush; Mateh Moshe 796; M”A 582/4; Omitted in Admur in SHU”A, although this is the Nussach in the Siddur]
 Correct pronunciation: One is to recite the word Lechaim with a Shva under the Lamed-Lechaim- and not with a patach under the Lamed [Lachaim]. The reason for this is because it sounds like one is saying “Lo Chaim” which means “no life”, and during these days [of Aseres Yimei Teshuvah], which are days of judgment, one must be particular in expressing his requests properly. However during the rest of the year we state Lachaim [Vehamideinu Malkeinu Lachaim] with a patach and we do not suspect for a mispronunciation as [G-d] follows the persons intention behind the word. [582/7]
 During the week the Nussach is Av Harachaman. However during Musaf, Mincha of Shabbos and Neilah the Nussach is Av Harachamim. [Siddur Admur; Peri Eitz Chaim Shaar R”H 6; Shaar Hakavanos 96b; Shaar Hakolel 9/7; Kaf Hachaim 582/34; Darkei Chaim Veshalom 710; See Likkutei Mahrich 62b; ] Rachaman refers to Z”A while Rachamim refers to Ava. [Likkutei Torah R.H. p. 62]
 Admur ibid; Michaber 582/5 regarding Zachreinu and Mi Chamocha; Rama ibid regarding Ukesov and Besefer; Rosh Brachos Perek 1; Ramban; Ran; implication of Rambam 2/10; Terumas Hadeshen 144; Levush; Bach; Kaf Hachaim 582/27
One is not to recite it as soon as he remembers and is not to repeat the blessing from the beginning. Doing so is forbidden due to it being a blessing in vain as these additions are merely an institution of the Geonim. [Admur ibid] One is not to conclude the blessing with Lamdeini Chukecha and then repeat it with the added verse. [Ruach Chaim 582/2; Ben Ish Chaiy Netzavim 20; Kaf Hachaim 582/31; see Shaareiy Tziyon 188/18] One is not to recite the verse prior to beginning the next blessing. [Elya Raba 582/11; Kaf Hachaim 582/30; Ben Ish Chaiy Netzavim 20; Yabia Omer 1/22; See M”B 114/32] One is not allowed to be stringent upon himself and repeat the blessing. [Darkei Moshe 582/4; M”A 582/4; Admur ibid] One is not to repeat Shemoneh Esrei even as a Nedava. [Machatzis Hashekel ibid; Kaf Hachaim 582/28]
Other Opinions: Tosafus [Brachos 12b] rules that these additions have the same status as Hakeil Hakadosh and hence if it was omitted one must return to that blessing or repeat Shemoneh Esrei. Practically most Rishonim and Poskim do not rule like this opinion. [See Kaf Hachaim ibid] Some Poskim rule that if one did not yet begin the next blessing he may say the omitted part after concluding the blessing prior to beginning the next blessing. [Ashel Avraham Butchach 582; Alef Hamagen 582/25] However many Poskim argue on this allowance and hold that doing so is considered an interval of the prayer. Thus one is to continue with the next blessing. [Simple implication from Admur and all other Poskim ibid and so rules Elya Raba 582/11; Kaf Hachaim 582/30; Ben Ish Chaiy Netzavim 20; Yabia Omer 1/22; See M”B 114/32]
 Kaf Hachaim 582/31
 One is not to go back and say it in its original place and then repeat from there. [implication of Admur ibid which states ”Bimakom Shenizkor”; Mateh Efraim 582/10 [regarding Ukesov]; however see M”E 602/8] So rules Admur also in 114/7 [regarding Mashiv Haruach]; However see 294/7 regarding Ata Chonantanu that one is to repeat from Vechoneinu Meitcha.
The reason: The reason for why one is not to go back to the original area is in order so one not repeat G-d’s name. [M”E ibid] To note however that this would only explain the stanza of Ukesov [which requires repeating from Vechol Hachaim] and not the other stanzas. Vetzaruch Iyun.
Other Opinions: Some Poskim rule that one may go back to the area of the addition and then continue from there as usual, and not from where he left off. This applies even though he may need to repeat the names of Hashem in that blessing. [M”B 582/16; P”M 114 A”A 8; 582 A”A 4; Ashel Avraham Butchach 582 Tinyana; Sdei Chemed Mareches Rosh Hashanah 3/3; Alef Hamagen 582/26; Kaf Hachaim 582/31] There is no worry of having to repeat Hashem’s name upon going back as one is not saying it as a blessing but simply as a supplication. [ibid]
 Kaf Hachaim 582/27 and 32; Ben Ish Chaiy Netzavim 20 [in name of Torah Leshma] writes that the verse of Zochreinu Lechaim is to be recited in Shomeia Tefila, although on Shabbos and Yom Tov one recites it prior to the second Yehi Ratzon. However Mi Chamocha is not a request and is hence not to be recited if it was omitted. The verse of Ubisefer is to be recited prior to the second Yehi Ratzon. The Kaf Hachaim 582/32 concludes that from other Achronim it implies that all the verses may be recited prior to the second Yehi Ratzon.
 Igros Kodesh 3/5 based on Rebbe Rayatz [brought in Shaareiy Halacha Uminhag 1/241; Shulchan Menachem 3/92]; Bnei Yisaschar Tishrei 2/23; Taamei Haminhagim 603 in name of Rav Sar Shalom of Belz; Mateh Efraim 584/10 [only mentions Ukesov and Bisefer]; See Otzer Minhagei Chabad 189
The reason: The last two stanzas of Ukesov and Ubisefer are requests from G-d and hence are befitting to be said by the congregation. However the stanzas of Mi Chamocha is a statement and not a request. Likewise the first stanza of Zechor is of lesser quality in comparison to the request the congregation recited in their private prayer of Ukesov and Ubisefer, and is thus not befitting to be said. [Rebbe ibid]
Other customs: Some communities are accustomed to recite aloud all four stanzas prior to the Chazan. [Likkutei Mahrich 68a; Yalkut Avraham 602; Piskeiy Teshuvos 582/8] Others are accustomed not to repeat any of the verses during the Chazan’s repetition. [custom of Gr”a Maaseh Rav 204]
 Siddur Admur; Baal Haturim; Shaar Hakavanos p. 96; Kaf Hachaim 582/33
 Siddur Rashash; Kaf Hachaim ibid
 Shaar Hakavanos ibid
 Siddur Rashash ibid
 Shaar Hakavanos p. 97; Kaf Hachaim 582/34