Bearing in mind that "Se'irim" implies two ('Mi'ut Rabim, Shenayim') why does the Torah insert the word "Sh'nei"?
Torah Temimah (citing Yoma, 62b): To teach us that, initially, the goats must be equal - in appearance, size and value. 1
And they must be purchased simultaneously (See Torah Temimah).
According to Rebbi (Yuma 70b), this is the ram of Musaf Yom Kipur (Bamidbar 29:8). Why is it mentioned, and the other Musafim are not?
Kol Eliyahu, Divrei Eliyahu: Vayikra Rabah (21:7) says that Aharon was permitted to enter the Kodesh ha'Kodoshim even not on Yom Kipur, with the Korbanos mentioned here. He needed a ram from the Tzibur, but not the other Musafim.
Rashi implies that he washes his hands and feet from the Kiyor. It says in Yuma (43b) that on Yom Kipur, he washes from a gold Kiton (flask)!
Moshav Zekenim (4) #1: Kiton is a Kiyor. It is called Kiton for it is smaller than the Kiyor [that was used the entire year - PF].
Moshav Zekenim (4) #2: Water of the Kiyor is not sanctified until it is put in the Kiton.
Here we do not discuss on Yom Kipur. (PF; refer to 16:32:1:2.)