I have two questions regarding the famous Gemoro (Yoma 21) that says that the Olei Regolim were squashed when standing but had plenty of room when bowing down ("Omdim Tzefufim UMishtachavim Revochim").
1) Rashi says that the bowing down was for Vidui. We generally say that there is no Vidui on Yom Tov. Does this Gemoro only then refer to Chol Hamoed?
2) When was this bowing down anyway?! We know that on Yom Kipur there were ten occasions when the Kohen Godol said the Shem HaMeforash and the people bowed down, but the Gemoro here refers to Yom Tov ("Olei Regolim"). Did all the people bow down at the same time during the Yom Tov proceedings at all? (Was the Shem HaMeforash used during Birkas Kohanim? - would they have said Vidui during Birkas Kohanim?) Does the Gemoro just refer to each person before he went out?
1) Rashi refers to the people's request for Mechilah. When they ascended to Yerushalayim for the Regel and they entered the Mikdash, each person would request his needs from Hash-m. (In fact, Rashi writes on this Mishnah as it appears in Avos (5:5) that the miracle occurred simply "so that no-one would hear his fellow man's *prayer*" -- his source for this is in Bereishis Raba 5:7). Certainly they took advantage of the opportunity of standing before Hash-m to ask, and their prayers included request for Mechilah, at which point they enumerated their sins in their prayers. That is the Viduy to which Rashi here is referring, which is not much different from the prayer to which Rashi in Avos refers.
We find, though, that the TASHBETZ (Teshuvos, 3:37) proves that this miracle occurred only on Yom Kipur, for that was the only Yom Tov we find that Viduy is mentioned with regard to the Avodah in the Beis ha'Mikdash. The SI'ACH YITZCHAK argues with this assertion and explains that the miracle occurred on the other festivals as well, but during their *Tefilah*. He agrees with the Tashbetz though that Rashi here, who says that they would bow during Viduy, is referring specifically to Yom Kipur (for there was no Viduy on other Regalim, as you asked).
Perhaps you are asking that it is *Asur* to say Viduy on Shabbos and Yom Tov, for one may not ask for his personal requests on those days. To that we could answer that it is certainly Mutar to say Viduy when there is a need to say it specifically on Shabbos, as the BE'ER HEITEV (OC 288:3) says. There is no better time to do Viduy than when everyone is standing in the Azarah on Yom Tov, before the presence of Hash-m. The MACHATZIS HA'SHEKEL (OC 288:13) cites the ROSH who says that it is even permissible to recite the 13 Midos of Rachamim on Shabbos when it is necessary to supplicate for rain. The MAGEN AVRAHAM there permits even falling on one's arm (as for Tachanun) on Shabbos. (Our Sugya is a very good support for his words.)
2) The Shem ha'Meforash was indeed uttered in the Beis ha'Mikdash during Birkas Kohanim, as we find in Sotah (38b). Rashi, though, does not suggest that the Gemara is referring to when they bowed down after hearing the Shem ha'Meforash because Hash-m would not perform a miracle for no reason. Rather, Rashi, and the Bereishis Raba, explain that they bowed during their Tefilah, and that is when a miracle happened in order to preserve their privacy. (It seems that they would bow during the Shemoneh Esreh from beginning until end out of honor for the Shechinah.)
The GEVURAS ARI (66a) asserts, by the way, that even though they mentioned the Shem ha'Meforash during Birkas Kohanim, nevertheless the people did not bow down at that point. He proves this from the Mishnah in Sotah (38a) which does not mention this bowing when it details the order of the Birkas Kohanim in the Mikdash. TOSFOS (Sotah 40b), however, writes explicitly that the people bowed during Birkas Kohanim just like they bowed during the Viduy of the Kohen Gadol on Yom Kipur.
In "KISVEI HA'GRIZ" he explains that the Gemara is referring to bowing upon entering the Azarah, for we derive from the Parshah of Bikurim that anyone who enters the Azarah must bow (VILNA GA'ON in Aderes Eliyahu to Parshah Ki Savo).