1) THE AFTERNOON TAMID ON YOM KIPPUR
OPINIONS: The Mishnah discusses the specific times during the day at which various parts of the Avodah on Yom Kippur are performed, such as the different Musaf offerings, the removal of the Kaf u'Machtah from the Kodesh ha'Kodashim, the afternoon Ketores and the afternoon lighting of the Neros.
The Mishnah, however, does not mention when during the day the afternoon Korban Tamid is offered. When is the afternoon Korban Tamid offered on Yom Kippur?
(a) RASHI (DH u'Par, and 70b, DH v'Achar Kach) explains that the afternoon Tamid is offered after the fifth Tevilah, which follows the Avodah of the removal of the Kaf u'Machtah (which is performed after the fourth Tevilah). The Tamid is offered immediately before the Avodah of the Ketores and the Neros.
The Beraisa later (Tana d'Vei Shmuel) provides support for Rashi's opinion. The Beraisa says that the Kohen Gadol offers his Ayil and the nation's Ayil, as well as the Emurei Chatas, after his third Tevilah, "but the Par ha'Olah, Shiv'as Kevasim, and Sa'ir ha'Na'aseh ba'Chutz (i.e., all of the remaining Musaf offerings) [are offered] together with the afternoon Tamid." The fact that the Beraisa differentiates between the time at which the Kohen Gadol offers his Ayil and the nation's Ayil, and the time at which he offers the afternoon Tamid, implies that he performs those Avodos at separate times (and one is performed after the fifth Tevilah). (See Chart #15, footnote 12, and Chart #16, footnote 6.)
(b) The RAMBAM (Hilchos Avodas Yom ha'Kipurim 4:2), however, rules that the Korban Tamid is offered after the third Tevilah, together with (i.e., right after) the Musaf offerings. The RAMBAN (Vayikra 16:32) adduces proof to this opinion from the wording of the Mishnah which mentions only the Ketores and the lighting of the Neros when it discusses what is done after the fifth Tevilah. If the Tamid is also offered after the fifth Tevilah, then the Mishnah should mention it together with the other routine, daily Avodos done at that point. On the other hand, if the Tamid is offered after the third Tevilah, the Mishnah does not need to mention it, as it leaves out a number of other Avodos done after the third Tevilah.
Further support for this opinion may be adduced from the next Beraisa which the Gemara cites. The Beraisa says that the Sa'ir ha'Na'aseh ba'Chutz is offered before the Kohen Gadol's Ayil and the nation's Ayil, after the third Tevilah. The Beraisa continues and says that after the Kohen Gadol offers his Ayil and the nation's Ayil, he burns the Emurei Chatas and, afterwards, he offers the afternoon Tamid. This implies that all of these Korbanos are offered after the third Tevilah. (This is in contrast to Rashi's understanding of the Beraisa. Rashi explains that when the Beraisa says, "afterwards, the afternoon Tamid is offered," it does not mean that it is offered at the same time as the previously-mentioned Korbanos, but rather it means much later, after the fifth Tevilah.)
In addition, the Mishnah says that the Sa'ir ha'Na'aseh ba'Chutz is offered with the afternoon Tamid. According to Rashi, the Mishnah must be arguing with the Beraisa, because the Mishnah maintains that the Sa'ir is offered after the fifth Tevilah and the Beraisa maintains that it is offered after the third Tevilah. (See Tosfos DH v'Achar Kach, and Chart #16, footnote 2.)
How does the Rambam understand the first Beraisa (Tana d'Vei Shmuel) which clearly supports Rashi's opinion when it says that the Korban Tamid is not offered after the same Tevilah as the Ayil of the Kohen Gadol?
RABEINU CHANANEL (cited by TOSFOS DH d'Tana) has a different Girsa in the first Beraisa. In our text of the Gemara, the Beraisa reads, "He offered his Ayil and the nation's Ayil and the Emurei Chatas [after the third Tevilah], but the Par ha'Olah, Shiv'as Kevasim, and Sa'ir ha'Na'aseh ba'Chutz together with the afternoon Tamid." According to the text of Rabeinu Chananel's Gemara, the Beraisa reads, "He offered his Ayil and the nation's Ayil and the Emurei Chatas and the Par ha'Olah, Shiv'as Kevasim, and Sa'ir ha'Na'aseh ba'Chutz together with the afternoon Tamid." That is, he offers all of these Korbanos, including the afternoon Tamid, after the third Tevilah. This apparently is the Girsa of the Rambam as well.
2) THE EIGHT BLESSINGS RECITED BY THE KOHEN GADOL
QUESTION: The Mishnah (68b) relates that the Kohen Gadol recited eight blessings in the afternoon of Yom Kippur when he read from the Torah. Those eight blessings included the familiar blessings of Birkas ha'Torah, Avodah ("Retzeh"), Hoda'ah ("Modim"), and Mechilas Avon (the central blessing of the Shemoneh Esreh of Yom Kippur), as well as four blessings which were unique to the Avodah of Yom Kippur: a blessing for the Mikdash, a blessing for Yisrael, a blessing for the Kohanim, and a blessing for Yerushalayim. The Mishnah adds that the Kohen Gadol then recited "the rest of the Tefilah."
The Gemara quotes a Beraisa which explains that "the rest of the Tefilah" refers to a prayer in which the Kohen Gadol beseeched Hash-m to protect the Jewish people. This prayer concluded with the blessing, "Shome'a Tefilah."
If the Kohen Gadol also recited the blessing of "Shome'a Tefilah," then he recited nine blessings and not eight. Why does the Mishnah say that he recited only eight blessings?
(a) In the text of the printed Mishnayos, the words "v'Al Yerushalayim" do not appear, nor do they appear in the Yerushalmi (Sotah 7:6 and Yoma 7:1). When the Beraisa lists the eight blessings, it does not include these words. The BACH and VILNA GA'ON delete these words from the Mishnah (68b) as well. Most of the Rishonim, including Rashi and the Rambam (Hilchos Avodas Yom ha'Kipurim 3:11), quote the Mishnah without these words.
Although Rashi in Sotah (40b) writes that "the Yerushalmi explains the blessing for Yerushalayim," the Yerushalmi makes no mention of such a blessing. Apparently, Rashi refers to the blessing for the Kohanim, because he does not explain that blessing anywhere else. (It is probable that the word "Yerushalayim" in the text of Rashi is a mistake, and it should read "Kohanim" instead.) Rashi means that the blessing for Kohanim is described in the Yerushalmi (which indeed it is). Accordingly, there are eight blessings (the blessing of "Shome'a Tefilah" is the eighth).
According to the Girsa that includes the words "Al Yerushalayim," perhaps the Mishnah merely uses these words to give another description for the blessing for the Mikdash, which, according to the Yerushalmi cited by the Rambam (Hilchos Avodas Yom ha'Kipurim 3:11), ends with the words "Shochen b'Tziyon" -- "Who dwells in Zion," a reference to Yerushalayim.
(b) The RAMBAM in Perush ha'Mishnayos (here and in Sotah) also omits the blessing "Al Yerushalayim," but he presents a slightly different way of counting the eight blessings. He counts Birkas ha'Torah, the blessing for the Torah, as two blessings. The Kohen Gadol recited one blessing before he read the Torah and a second blessing after he read the Torah. He counts the blessing for Yisrael and the blessing of "Shome'a Tefilah" as one blessing: the Kohen Gadol prayed that Hash-m protect the Jewish people and he concluded his prayer with the words "Shome'a Tefilah," as the Beraisa here mentions. This is the eighth of the eight blessings.
The Rambam's text of the Mishnah apparently lists the blessing for Kohanim before "Al Yisrael" and "the rest of the Tefilah." Since those two blessings are listed consecutively ("Al Yisrael and the rest of the Tefilah"), the Rambam understands that they are counted as a single blessing. (However, in Hilchos Avodas Yom ha'Kipurim (3:11), the Rambam explains the Mishnah like the Rishonim cited above in (a), and he places the blessing for the Kohanim after the blessing for Yisrael.)
(c) The ME'IRI cites Rishonim who have the text of "Al Yerushalayim" in the Mishnah, and he writes that according to this Girsa the last blessing ("Shome'a Tefilah") is a general prayer and is not included in the count of eight blessings. (See also Insights to Sotah 40:4.)