1. Mistakes-Blew the wrong sound:
Blew a Teruah instead of a Shevarim or vice versa: In all cases that one was supposed to blow a Teruah or Shevarim and instead he blew a Shevarim or Teruah [i.e. one blew a Shevarim inתר”ת instead of a Teruah, or a Teruah in תש”ת instead of a Shevarim] he must start again from the Tekiah of that particular set. [Each of the three groupings in תשר”ת/תש”ת/תר”ת is considered a set for a total of 9 sets] This applies even if one only began the wrong blow, and then remembered right away.
If in תשר”ת one began blowing the Teruah before blowing the Shevarim: If one began blowing the Teruah prior to finishing blowing the 3 blows of the Shevarim, then if it was all done in one breath he does not need to re-blow the Tekiah of that set. Rather he is to simply reblow the Shevarim-Teruah. If however one took a breath in between the Shevarim and Teruah, or began blowing a Teruah before even beginning the Shevarim, he must start again from the Tekiah of that particular set.
Blew an extra set of Teruah or Shevarim: In all cases that one is supposed to blow a Shevarim or Teruah and he blew a second set. Then if the first set was Halachically valid he must repeat from the first Tekiah of that set, if he took a breath between the two sets. This applies even if he did not complete the second set, such as he only blew one Shevarim or one Terumatin. If, however, one did not take a breath in between the two sets, or if the previous set was not Halachically valid then he may continue with the last Tekiah of that set.
2. Restarting an off pitched sound-If one blew a Teruah or Shevarim and stopped in middle, such as due to that the sound was not going well, may he restart the Teruah or Shevarim without repeating the first Tekiah?
If the ill sounding blow was Halachicly valid [i.e. contained the minimum required length according to even the first opinion in Halacha 7] and he then took a breath and blew a second time, he must repeat from the first Tekiah of that set. If, however, one did not take a breath in between the two blows, or if the previous blow was not Halachicly valid, then he may continue with the last Tekiah of that set. Thus, practically speaking, if one for example blew at least three Terumatin of a Teruah and it wasn’t blowing well and he took a breath and started again, then he is to begin again from the Tekiah of that set.
3. Who says the Bracha on Mivtzaim?
Blowing for other men: One who has already heard Shofar, or plans to fulfill the Mitzvah with a later blowing, should have the listener say the blessing. If, however the listener is a man and is unable to say the blessings himself then one may say both blessings for him. [On the second day when Rosh Hashanah does not fall on Shabbos, men of Sephardic origin do not say the Shehechiyanu blessing.]
Blowing for only Women: If one is blowing for only women, [then if the women are of Ashkenazi custom], she is allowed to say the blessings herself. If she cannot say the blessing herself one may not say the blessings for her. [If she follows the Sephardi custom, then she is not to make the blessing at all.]
See Chapter 2 Halacha 9 for the full details of this subject!
It is important to remind those hearing Shofar to have in mind to fulfill the Mitzvah of Shofar, as Mitzvahs require Kavana. See Chapter 2 Halacha 3 for the full details of this subject!
5. When is the Shofar to be blown?
Daytime: The Shofar may only be blown during the daytime of Rosh Hashanah. The entire day is valid for blowing Shofar.
From what time of day may one begin blowing Shofar? One may blow Shofar beginning from sunrise. If one blew before sunrise but after the beginning of dawn [Alos Hashachar] he has nevertheless fulfilled his obligation and is not required to hear Shofar a second time. [Furthermore in a time of need one may even initially be lenient.] If one began blowing right before Alos and the sound continued past Alos, that sound is invalid. This applies even if it contained the minimum required sound from after Alos.
Until what time may one blow Shofar? One may blow Shofar until Tzeis Hakochavim. [Regarding if a blessing is made when blowing past sunset-See Q&A]
Blowing within the first three hours of the day: If one is blowing Shofar on Rosh Hashanah without a Minyan in order to fulfill the Mitzvah, he is to beware to delay the blowing of the Shofar until three hours have passed from the beginning of the day. [This is commensurate to Sof Zeman Kerias Shema. Thus, one should not blow Shofar until after Sof Zerman Kerias Shema. Some Poskim write that in today’s times it is proper not to blow the Shofar even with a Minyan until after three hours have passed. All the above however applies in a case that one will be able to blow or hear Shofar later on past the 3rd hour of the day. If, however, one may not have an opportunity to hear it later on, then certainly it may and should be blown prior to 3rd hour of the day. Accordingly, those doing Mivtza Shofar to merit as many Jews as possible in the Mitzvah may begin doing so from as early as sunrise. Likewise, those who need to eat before Shacharis due to medical reasons may blow the Shofar even within Zeman Kerias Shema for this purpose.]
One may blow Shofar from sunrise until Tzeis Hakochavim.
May one blow the Shofar past sunset?
One may blow Shofar after sunset until nightfall. After nightfall it is forbidden to blow the Shofar. Seemingly, this applies likewise on the 2nd day of Rosh Hashanah, that one may blow until nightfall.
Is a blessing recited? Some Poskim rule a blessing is not to be recited when blowing Shofar between sunset and Tzeis. Other Poskim rule that on the first day one may blow with a blessing between sunset and Tzeis. However, on the second day one must blow without a blessing.
6. Must the blower and listeners be in the same area/building/room?
One can be Yotzei Shofar even if he is not in the same area as the blower, so long as an echo is not sounded. Thus, a person can blow Shofar for a family from outside their home and have them be Yotzei by hearing the blows from inside. Likewise, people may stand outside the Shul and hear the blowing and be Yotzei. Likewise, the blower may stand outside the Shul and be Motzi those inside the Shul. Regarding if one can be Yotzei outside if the blowing is taking place in an underground, or basement Shul-see Q&A!
 588:1; Michaber 588:1
 The reason: This is learned from the verse “Yom Teruah” that the Teruah must take place during the day and not night. [Admur ibid; Megillah 20b]
 The reason: Biblically, day begins from Alos Hashachar regarding all Halachic matters. Nevertheless, the Sages decreed that one must delay blowing the Shofar until after sunrise being that not all people are expert in the definition of Alos and hence in order to be assure that it is day one must wait until sunrise. [Admur ibid; Rashi Megillah ibid] In 488:3 Admur writes as follows: As it appears like night in the eyes of the masses.
 Kaf Hachaim 588:8 regarding one who is traveling based on Gemara Brachos 30a
 587:4; 588:2
The reason: The reason for this is because every blow must be valid in its entirety, from beginning to end, for it to be considered a Kosher sound. Hence since in this case the sound only became valid in its middle, it therefore is not considered a Kosher sound. [587:4]
 Admur ibid; Mishneh Megillah 20b; So also writes Admur 488:3 regarding Halel
 591:14; M”A 591:9; M”B 591:15; Kaf Hachaim 591:36
 The reason: The reason for this is because within the first three hours of the day G-D does not judge beyond the letter of the law, as during this time He learns His Torah which is called Truth [and thus judges people in accordance to Truth]. There is thus to worry that perhaps the supernal courts will investigate his actions and his prayers [Tekios] will be denied. However, after three hours into the day He judges the entire world and once He sees that the world cannot up stand to His judgment He therefore judges them in a manner of above the letter of the law, and the individuals prayer will not be differed. [ibid]
 Machazik Bracha 588:1; Mateh Efraim 588:2; Kaf Hachaim 588:6
 Admur 588:1; Chayeh Adam 141:1; Mishneh Berurah 588:1; Kaf Hachaim 588:2.
 So is implied from Stimas Haposkim brought above. However, Tzaruch Iyun as why do we not say Safek Derabanan Lehakeil, and hence there is no longer an obligation to blow by Bein Hashmashos which is questionably day/night. This would be similar to the ruling that on the 2nd day one who is in doubt as to whether he heard Shofar is not required to blow. However perhaps there is a difference if the doubt is in whether one already heard the actual blowing, or if one for certain did not hear the blowing but is in doubt if the Mitzvah still applies.
 Chayeh Adam 141:1; 144:20; Mishneh Berurah 588:1; Kaf Hachaim 588:2; 600:12; Regarding Lulav: M”A 658; Regarding Megillah: M”B 687:5; Kaf Hachaim 687:9; P”M 692 M”Z 3
 Michtam Ledavid 17; Birkeiy Yosef 600:5, brought in Kaf Hachaim 600:11
Opinion of Admur: Admur ibid rules that from Alos until Tzeis is the permitted time for blowing Shofar. So, writes Admur also regarding Halel in 488:3. The source of Admur is from the Gemara Megila 20b which states that until Tzeis Hakochavim it is considered day. This seems to imply that during Bein Hashmashos one may blow even with a blessing! This is further inferred from the change of wording from the Tur which writes simply “until night” while Admur specifies Tzeis. Vetzaruch Iyun Gadol, as Bein Hashmashos is questionable whether it is night or day as rules Admur is 261:1, hence how can one say a blessing at that time.
 Admur 587:5; Taz 6587:1; Chayeh Adam 141:5; M”E 587:1; Kaf Hachaim 587:6