Making Kiddush on wine which was left opened:
One may not recite Kiddush over wine that has been left open/revealed.
If it stayed opened for only a short amount of time: Nevertheless, if the wine remained open/revealed for only a short amount of time, one does not need to be so stringent to avoid using it. This especially applies in these countries where wine is not that common to find. If, however, the smell and taste of the wine has gone off, then it may not be used.
Summary [includes points explained in Q&A]:
One may not make Kiddush over wine which was left open for a long time. If, however, it was left open for only a short amount of time, it remains valid. [However, initially it should not be uncovered for even a short amount of time. Accordingly, one is to cover the wine bottle as soon as he finishes pouring from it and is not to leave it open even momentarily, and so is the worldly custom. Likewise, one is to recite Kiddush as soon as the wine is poured into the cup, and is not to pour the wine prior to being ready to say Kiddush. In the event that the wine bottle was not covered while making Kiddush, then if it was left open for only a short amount of time, it may be used even initially for another Kiddush.]
May one even initially [Lechatchila] leave Kiddush wine open for a short amount of time?
One is not to initially leave the wine open for even a short amount of time. Accordingly, one is to cover the wine bottle as soon as he finishes pouring from it and is not to leave it open even momentarily, and so is the worldly custom. [Likewise, one is to recite Kiddush as soon as the wine is poured into the cup, and is not to pour the wine prior to being ready to say Kiddush.]
Must one cover the wine bottle during Kiddush and may the wine still be used if it was left open?
Initially, as explained above, it is best for the wine that is used for Kiddush to always remain covered, and hence one is to cover the wine bottle as soon as he finishes pouring from it and is not to leave it open even momentarily, and so is the worldly custom. [Likewise, one is to recite Kiddush as soon as the wine is poured into the cup, and is not to pour the wine prior to being ready to say Kiddush.] This applies before, during and after Kiddush and is not limited to only while making Kiddush. Many however are particularly careful in this regard during Kiddush based on a tradition of the Baal Shem Tov that the wine is to be covered especially during the time that Kiddush is said.
Bedieved: In the event that the wine bottle was not covered while making Kiddush, then if it was left open for only a short amount of time, it may be used even initially for another Kiddush.
How long is considered “left open for a long time” which invalidates the wine for Kiddush?
Some Poskim rule that if the wine was left open for even 3-4 hours it is still valid. Other Poskim rule it is up to 5-6 hours. Other Poskim rule that if it was left open for the entire night it is invalid. Other Poskim rule that it is all dependent on the wine and as to whether it’s taste or smell has dissipated with the time that it was left open. Practically, it is only invalid if it was left open throughout the night, or long enough for its smell/taste to dissipate.
If the wine was left open in a fridge or closet, is it invalid?
If the wine was left open inside a closed area, such as a fridge or closet, it is valid so long as its taste/smell has not dissipated.
If one has no other wine available, may he make Kiddush on wine which was left open for a long time?
Some Poskim rule one may not use such wine even if no other wine is available, and Bedieved if such wine was used he does not fulfil his obligation. Other Poskim, however, leave this matter in question. Other Poskim rule that if he already used the wine then he fulfills his obligation and is not required to repeat the Kiddush. Practically, [by nighttime] he is to try to hear Kiddush again from another person.
May wine that was left open be used for the day Kiddush, Havdala or Kos Shel Bracha?
Some Poskim rule that wine that was left open for a long time is invalid for any Kos Shel Bracha, including both the night and day Kiddush and Havdala. This applies especially to the wine used for Sheva Brachos. Other Poskim however rule that possibly one may recite the day Kiddush, Havdala and other Kos Shel Bracha on revealed wine, and the above ruling only applies to the night Kiddush.
Wine Decanting & Aeration: May one open the wine bottle and leave it open for several hours in order for it to be able to “breath,” and improve its taste and quality?
 Admur 272:1; Michaber 272:1; Bava Basra 97b
 The reason: Although today we are no longer careful against drinking revealed liquids, being that snakes are no longer commonly found, nevertheless [it is not to be used]. [Admur ibid; Michaber ibid; Tur in name of Maharitz Geios] This is due to the obligation to “offer G-d the most pleasant items…” and thus the wine must be fit to serve to princes and aristocrats. [Admur ibid; M”A 272:1; Taz 272:2; M”B 272:3; Bach 272; Rebbe Nechmia in Bava Basra ibid] The reason why revealed wine is not considered pleasant before Hashem or fit for aristocrats is because a) Leaving it open causes its taste and smell to dissipate. [Admur ibid; M”A ibid] and b) Leaving it open can allow dirt and insects to fall inside. [Divrei Malkiel 4:1; Pesech Hadvir 272:2; See Kaf Hachaim 272:11]
Other reasons: The wine is not to be left open being that it corresponds to the “Yayin Hameshumar” which Hashem will give us in the future and hence the wine used for Kiddush is to be guarded. [Minchas Shabbos 77:18 in name of Toras Chaim Bab Basra 97b “Even a small amount of time one is to be particular”; Brought in Tosefes Shabbos 242:5; Daas Torah 272; Piskeiy Teshuvos 272:2 footnote 9]
 Admur ibid; M”A ibid; Elya Raba 272:3;Chayeh Adam 6:7; Chesed Lealafim 272:1; Kaf Hachaim 272:7
 The reason: As even the aristocrats and ministers are not particular in this after the fact [and they still drink the wine that was revealed for only a short period] unless the smell and taste of the wine has gone off [and thus it is no longer considered unfit to be brought to the king]. [Admur ibid; M”A ibid]
 This however applies also today that wine is commonly found. Shaar Hatziyon 272:5 in implication of M”A and Admur ibid; See Ketzos Hashulchan 80:1 who does not differentiate in this matter
 Implication of Admur and M”A ibid; Minchas Shabbos 77:18 in name of Toras Chaim Bab Basra 97b “Even a small amount of time one is to be particular”; Tosefes Shabbos 242:5; Daas Torah 272; Kaf Hachaim 272:7; Az Nidbaru 1:7; Piskeiy Teshuvos 272:2; Orchos Rabbeinu that so was custom of Stepler
Implication of Admur: The following implications from Admur lead one to conclude that initially the wine is not to be uncovered even for a short amount of time: a) Today wine is commonly found, and Admur partially based his allowance on the scarcity of wine back then. [See Az Nidbaru ibid] b) Admur here writes one does not need to be so stringent, thus implying that there is room to initially be stringent. [See Az Nidbaru ibid] c) The aristocrats would only drink it after the fact, implying that initially they would be careful to cover the wine d) Why rely on a leniency if it can be avoided, and Admur was only referring to the law of after the fact when it was already left revealed.
 Az Nidbaru 1:7; Hakashrus 18:16 footnote 72 “The custom is to cover the bottle immediately after pouring out the wine and not to leave it open at all.”; Piskeiy Teshuvos 272:2
 Minhagei Kunruna 184; Az Nidbaru 1:7; Hakashrus 18:16 footnote 72 “The custom is to cover the bottle immediately after pouring out the wine and not to leave it open at all.”; Nitei Gavriel Pesach 2:235; Piskeiy Teshuvos 272:2; Harav Eli Landa in an email correspondence; So write specifically regarding the night Kiddush: Chochmeiy Yisrael Besht p. 118 [printed in 1922 from letters discovered in a Geniza, which were bought by one of the Guraries and given to the Rebbe Rashab as a gift] “I heard from him [the Besht] that one is to close the wine bottle with its cover after pouring the wine into the cup for the night Kiddush”; Reshimos Devarim [Chitrik] 1:9
 Pashut, and so I was told by Harav Eli Landa that the custom is to be always careful and not only during Kiddush; See tradition of Besht in previous footnote which explicitly says to cover the wine after it is poured into the cup and not specifically during the recital of Kiddush
The reason: According to the reason of “revealed wine” brought in Admur 272:1, there is no difference between before, after or during Kiddush in this regard. Those that are accustomed to only cover the wine while making Kiddush, and leave it open until they begin Kiddush, or after Kiddush, during the meal, seemingly have no basis for their custom, as there is no reason for why the wine must be covered during Kiddush other than due to the reason of “Giluiy.” Making Kiddush in the presence of an open bottle does not make the wine Pagum, and does not cause the wine to be any worse than any other wine, other than the fact it was left open, which is relevant to be before and after Kiddush as well.
 See Chochmeiy Yisrael Besht p. 118 [printed in 1922 from letters discovered in a Geniza, which were bought by one of the Guraries and given to the Rebbe Rashab as a gift] “I heard from him [the Besht] that one is to close the wine bottle with its cover after pouring the wine into the cup for the night Kiddush”; Reshimos Devarim [Chitrik] 1:9; To note that the emphasis of the tradition of the Besht is specifically regarding the night Kiddush!
 As rules Admur 272:1 that momentary openness does not disqualify the wine. Likewise, making Kiddush in the presence of an open bottle, which is considered as if he made Kiddush on the bottle as well [See Admur 271:28] does not make the wine Pagum, and does not cause the wine to be any worse than any other wine, other than the fact it was left open, which is relevant to be before and after Kiddush as well. Thus, one may even initially use this wine for Kiddush even though it was left open during Kiddush and had Kiddush said over it as wine only becomes Pagum when one drinks from it and not when one says Kiddush over it. [See Admur 182:4 and 190:5 and 272:19-20]
 Ketzos Hashulchan 46 footnote 2
 The reason: Admur does not specify any amount of time, although, one can learn from the Seder on Pesach that it is at least 3-4 hours being that the second cup is poured at the beginning of Maggid and not drunk until the end. [Ketzos Hashulchan ibid; See Az Nidbaru 1:7]
 Divrei Malkiel 4:1 that 20 minutes is a short time and it takes 5-6 hours long for the wine’s taste to dissipate; See Az Nidbaru 1:7; Piskeiy Teshuvos 272:2
 Beis Yehuda 53; Ben Ish Chaiy Bereishis 2:25; Kaf Hachaim 272:7; Aruch Hashulchan 272:5;
 Implication of Admur ibid and Chayeh Adam 6:7; Minchas Shabbos 77:18; Piskeiy Teshuvos 272:2
 Kaf Hachaim 272:9
 Birkeiy Yosef 272:1 in name of Ramban; Machaneh Yehuda 230; Pesach Hadvir 272:4, brought in Kaf Hachaim 272:10; M”B 272:1 in name of Shaareiy Efraim and Ramban brought in Beis Yosef; Kesav Sofer 88
 Biur Halacha 272:1 “Ein Mekadshin”
 Kaf Hachaim ibid; Piskeiy Teshuvos 272:2
 Birkeiy Yosef 272:1 in name of Beis Yehuda 43; Aruch Hashulchan 272:5; M”B 272:1 and Biur Halacha 272:1 “Al Yayin”; Kaf Hachaim 272:8
 Ruach Chaim, brought in Kaf Hachaim 272:11
The reason: As the Satan especially prosecutes during a time of Simcha. [ibid]
 Rav Akiva Eiger 272 based on Michaber 272:4
Background: Red wine is aerated by opening the bottle in advance of service. Aeration removes from the bottle musty odors, such as those from an unclean barrel. The amount of time red wine needs for aeration depends on the age of the wine. Young red wines, usually those under 8 years old, are strong in tannic acid and require 1 to 2 hours to aerate. Mature red wines, generally those over 8 years old, are mellow and need to breathe for approximately 30 minutes, if at all. Very old red wines require no aeration. Wines with delicate bouquets, such as white wine, rose, champagne, and sparkling wines are not aerated and are opened just before service. The narrow neck of the wine bottle may not permit sufficient aeration. If you really want to aerate your wine, pour it into your glass, swirl it around, and let it sit for a while. A wine can require decanting for two reasons: It needs aeration or it needs to be separated from sediment that has settled with aging. For breathing purposes, simply pour the bottle of wine into a decanter for serving. Decanting to remove sediment is a delicate process. [https://www.thoughtco.com/why-you-should-aerate-wine-4023740]
 The reason: As the main reason behind the restriction against leaving it open is so the wine does not spoil or lose taste. Accordingly, if the wine actually tastes better upon leaving it open, then there should be no problem involved in doing so;
 The reason: As the allowance would only apply according to the main reason mentioned behind the Halacha. However, according to the other reasons mentioned in Achronim [so insects don’t fall inside, and so it be like the wine of the future which is guarded] seemingly it should remain covered even in a case that one intends to benefit the wine. Thus, in my conclusion, I would say that from the letter of the law it is allowed, although it is still good to be stringent.