Yoma, Chapter Five, Mishnah Seven
This mishnah basically completes the sacrificial aspects of the Yom Kippur service. It teaches that the order in which the acts must be performed is preciseone act cannot be moved up in front of another. The mishnah then discusses the consequences if one act is moved up before another.
1) Concerning every act of Yom Hakippurim mentioned in the prescribed order [in the mishnah]: if he performed one [later] act before an [earlier] one, it is as if it had not been done at all.
2) If he dealt with the blood of the goat before the blood of the bull, he must start over again, and sprinkle the blood of the goat after the blood of the bull.
3) If before he had finished the sprinklings within [the Holy of Holies] the blood was poured away, he must bring other blood, and start over again and sprinkle again within [the Holy of Holies]. Similarly, in the Hekhal and the golden altar, since they are each a separate act of atonement.
4) Rabbi Elazar and Rabbi Shimon say: wherever he stopped, there he may begin again.
Section one: The mishnah is adamant that all of the acts that were described in the previous sections be performed in the order in which they were prescribed. The remainder of the mishnah now explains what he must do if the high priest performed one of the acts out of order.
Section two: If he sprinkled the goats blood before he sprinkled the bulls blood he must start over again and sprinkle the bulls blood and then the goats blood. The Talmud explains that this refers to the sprinkling done in the Hekhal. If he sprinkled the goats blood inside the Holy of Holies before the bulls blood, he must sacrifice a new goat because he must sprinkle the bulls blood inside before he even slaughters the goat.
Section three: If the blood was poured out before he finished sprinkling inside the Holy of Holies, he must go back and slaughter another animal, be it the bull or the goat. This is true even if he already sprinkled six out of the seven times. In other words, all of the sprinklings must be done with the blood of the same animal. However, if he finished sprinkling inside and was sprinkling in the Hekhal when the blood spilled, he need not go back and redo the inside sprinklings. The same holds true with regard to the sprinkling on the golden altar in the Hekhal. Each of these sets of sprinklings is considered independent, such that if one is interrupted the earlier one need not be redone.
Rabbi Elazar and Rabbi Shimon go a step further. If the blood is spilled in the middle of a set of sprinklings, he must slaughter a new animal but his earlier sprinklings count. He begins exactly where he left off. For Rabbi Elazar and Rabbi Shimon each sprinkling is its own entity and hence a sprinkling that has already been performed correctly need not be redone, even if the subsequent ones are done with the blood of a different animal.