Seeing as Aharon now had to enter the Kodesh ha'Kodashim to take out the Kaf and Machtah, why does the Torah write "U'va Aharon el Ohel Mo'ed", and not ' ? el me'Beis la'Paroches'?
Oznayim la'Torah (citing the Meshech Chochmah): To teach us that Aharon had to enter the Kodesh Kodashiim via the Heichal and not from the entrance at the back of the Kodesh ha'Kodashim. 1
See Oznayim la'Torah.
Why did Aharon enter the Kodesh Kodashim for the second time?
Why does the Pasuk invert the order of events?
Ramban: Because it is currently discusses Avodos ha'Yom in the Bigdei Lavan, 1 which it completes (before discussing the Avodah in the Bigdei Zahav - the rams of the Olos).
Refer to 16:23:2:2.
Which Avodos were performed after the last Tevilah?
Rashi (from Toras Kohanim): Aharon brought some of the Musafim before he took out the Kaf and the Machtah. After taking them out, he immersed for the last time and offered the rest of the Musafim, the afternoon Tamid and afternoon Ketores wearing the Bigdei Zahav. 1
Aharon brought the Olos after his Chatas, since a Chatas always precedes an Olah, but why did he bring them after the Sa'ir la'Azazel?
Why does the Torah need to insert the (otherwise superfluous) words "Asher Lavash"?
Yoma 32a: To compare taking off a set of Begadim to putting on the other one - Just as the latter required Kidush Yadayim ve'Raglayim, so too did the former.
Yoma, 71a: It means 'which he had worn earlier' - to teach us that he now changed a second time into the Bigdei Lavan after he concluded the Avodas ha'Yom, before taking out the Kaf and Machtah. 1
Oznayim la'Torah" "asher Lavash", 've'Lo Elb'shem Od' - To teach us that the Bigdei Lavan required Genizah and may not be worn again. 2
What are the ramifications of "Ve'hinicham Sham", mentioned in connection with the four Bigdei Lavan?
Rashi, Seforno and Targum Yonasan 1 : It means that, after removing the Kaf and Machtah and changing into the eight Begadim of a Kohen Gadol, he had to leave the white ones there 2 , never to be used again, 3 not by a Kohen Hedyot during the year nor by Aharon on the following Yom Kipur. 4
See Peirush Yonasan.
In the Heichal.
Since they were used for an Avodah that attained a high level of Kedushah, it is befitting that, once that Avodah is concluded, they are put away and not used again on another occasion (Seforno).
Refer also to 16:23:5.1:3.
In Yuma 32a, it asks why Aharon entered, and says 'to take out the spoon and pan.' The verse says that he entered the Ohel Mo'ed to remove his garments! And the spoon and pan were in the Kodesh Kodashim!
Ramban: We cannot say that he enters merely to remove his clothes! Rather, it was for Avodah, i.e. to take out the bowl and the pan, which he had brought in earlier with the Ketores.
QUESTIONS ON RASHI
Rashi writes that the verses are out of order. What forces us to say so?
Rashi and Ramban (based on Yoma, 32b): We have a tradition that on Yom Kipur, the Kohen Gadol Tovels five times and washes his hands and feet ten times, 1 in which case, as things stand, there are only three Tevilos and six washing of the hands. Consequently, we are forced to invert the Pesukim and to insert the Olah of Aharon and that of the people (in Pasuk 24) here, so that Aharon Tovels, changes to Bigdei Zahav and brings the Olos 2 and afterwards changes back, before he finally enters to take out the Kaf and the Machtah.
Kol Eliyahu and Divrei Eliyahu: Until now, the Torah discussed Aharon's Heter to enter the Kodesh ha'Kodashim even not on Yom Kipur, with the Korbanos mentioned here (Vayikra Rabah). Then, he did not need to Tovel five times and everything is in the correct order. After Aharon [died], it is permitted only on Yom Kipur, 3 and the Kohen Gadol is obligated to Tovel five times, so we must change the order to obligate another change of Begadim.
Riva: If all Avodas P'nim was performed at once, he would need to wear Bigdei Lavan only once, and need only three Tevilos! (Now, he must wear them twice, and the Bigdei Zahav three times. He Tovels before wearing Bigdei Kehunah each time, and washes hands and feet each time he wears them and each time he removes them. - PF)
And some of the Musafim (Rashi).
Kol Eliyahu and Divrei Eliyahu: This is why it mentions 'on Yom Kipur' and 'once a year only now.
Rashi writes that the verses are out of order. Within one matter, the Torah is in order!
Moshav Zekenim (from Yuma 32a): Even within one matter, when there is a proof, the Torah is not in order.
Rashi writes that he enters afterwards to take out the Kaf and the Machtah. One may not enter without need! He could leave them there, and next year he will enter with a new pan, and when he leaves, he will take out the old pan!
Riva citing R. Tam of Orai': It would be disgraceful to leave the empty pan there. Chachamim permitted moving a pan with ashes for it is repulsive to people. All the more so, we should remove it from in front of Hashem!