An Avodah done out of sequence is meaningless.

If he did the Haza'ah of the Dam Sa'ir before the Dam Par, he must do the Haza'ahs Dam Sa'ir again.

If the rest of the Dam (Shirayim) was poured out before he completed the Matanos, he must slaughter a new Par and start that Avodah again;

The same will hold if it was poured out during the Haza'os in the Heichal, whether on the Paroches or on the Mizbe'ach ha'Zahav.

Each one is a separate Avodah which, once completed, need not be repeated.

R. Elazar and R. Shimon maintain that he need not even go back to the beginning of that Avodah, rather, he resumes where he left off.

(R. Yehudah): Only the order of the Avodos in the Kodesh ha'Kodoshim (done in Bigdei Lavan) is Me'akev (not those done in Bigdei Lavan outside of the Kodesh ha'Kodoshim).

(R. Nechemyah): The order of all Avodos done in Bigdei Lavan is Me'akev (inside or out).

(R. Yochanan): Both of these opinions derive from the application of the word "Chukah" in the Pasuk:

R. Yehudah would say that "Chukah" refers to the place where the once a year Kaparah occurs.

R. Nechemyah understands that "Chukah" refers to all those Avodos which bring atonement once a year.

Question: But place does not appear in the Pasuk!?

Answer: Rather, R. Yehudah derives from the limiter words "Zos" and "Achas" that "Chukah" is not speaking about Bigdei Lavan outside, nor about Bigdei Zahav.

Question: What will R. Nechemyah learn from these limiters?

Answer: One excludes Bigdei Zahav and the other excludes Shirayim (which were poured later than its proper turn).

Question: Whence will R. Yehudah know the Din that the order is not Me'akev the Shirayim?

Answer: Shirayim follows the other Avodos done in Bigdei Lavan (and will be Me'akev, as they are).

R. Yehudah's Din is found as one opinion in the Beraisa:

R. Akiva learns the Pasuk "Kiper-Kilah" (as explained below).

R. Yehudah learns (with the order of the Pasuk) "Kilah-Kiper".

Their meaning is the subject of a Machlokes R. Yochanan and R. Yehoshua b. Levi.

One view holds that all agree that Shirayim are not Me'akev and the argument revolves around how to decode the Pasuk.

According to the other view, the argument is over the issue of Shirayim being Me'akev (hence the position of R. Yehudah).

Question: But we find R. Yochanan teaching that R. Nechemyah (who interprets "Chukah", as does R. Yehudah) is of the view that Shirayim are Me'akev (yet here [in 2.c.] he says that, according to R. Nechemyah, Shirayim are not Me'akev!?

Answer: Good question.

(R. Chanina): Chafinah of the Ketores done before the Shechitah of the Par is meaningless.

Question: This seems to depart from the view of R. Yehudah who holds that "Chukah" only applies to Avodos which are done in Bigdei Lavan within (and Shechitah is not done there)?

Answer: Even according to R. Yehudah, Shechitah is needed for the Avodas P'nim and is considered as such.

Question: Then the Mishnah (in 1.c. above) should require a new Chafinah in a case where we needed to slaughter a new Par for the Hazaos!?

Answer: The Tana was only dealing with the Hazaos (and not with the Ketores at all, whose Chafinah would, indeed, need to be repeated -Rashi).