Yadayim, Chapter Four, Mishnah Two
Most of this mishnah is found word for word in Zevahim 1:1 and 1:3. Most of my commentary here is the same as that there. It is brought here as well because according to this mishnah, those halakhot from Zevahim originated on that same famous day.
1) On that day they said: all animal sacrifices which have been sacrificed under the name of some other offering are [nevertheless] valid, but they are not accounted to their owners as a fulfillment of their obligations, with the exception of the pesah and the sin-offering.
2) [This is true of] the pesah in its correct time and the sin-offering at any time.
3) Rabbi Eliezer says: [with the exception] also of the guilt-offering; [so that this refers to] the pesah in its correct time and to the sin- and guilt-offerings at any time.
4) Rabbi Shimon ben Azzai said: I received a tradition from the seventy-two elders on the day when they appointed Rabbi Elazar ben Azariah head of the college that all animal sacrifices which are eaten and which have not been sacrificed under their own name are nevertheless valid, but they are not accounted to their owners as a fulfillment of their obligations, with the exception of the pesah and the sin-offering. Ben Azzai only added [to these exceptions] the wholly burnt-offering, but the sages did not agree with him.
Section one: For most sacrifices, if the priest offering them thinks that he is offering a different sacrifice than he is really supposed to be offering, the sacrifice is still valid. This means that its blood can be spilled on the altar and the sacrifice can be eaten by those who would have been able to eat it had it been offered properly. However, the sacrifice does not count as far as fulfilling the obligation of its owner. Thus if the owner was obligated to bring an olah, for instance, and it was sacrificed with the intent of it being another sacrifice, the owner must bring another olah in its place.
The exception to this is the pesah and the hatat. If either of these two sacrifices is offered with the intent of its being a different type of sacrifices, not only does it not count for the owner who brought it, it is completely disqualified. Its blood cannot be spilled on the altar, nor can it be eaten.
Section two: The pesah is only disqualified if it is slaughtered with the wrong intent at the time that it is supposed to be slaughtered, on second half of the day on the fourteenth of Nissan. If it is slaughtered on the wrong day, for the wrong purpose, then paradoxically, it is valid, although it would obviously not count for its owner. Its as if the mishnah is saying that in this case, two negatives can make a positive. When it comes to the hatat, there is no specific time in which it must be offered. Therefore, no matter when it is offered, if the intention is for the wrong sacrifice, it is disqualified.
Section three: Rabbi Eliezer argues that the same rule that applies to the hatat applies to the asham, also a sacrifice brought to atone for sin. If it is slaughtered for the sake of it being a different sacrifice, it is disqualified.
Section four: This section is found in Zevahim 1:3. My commentary here is the same as it is there.
In section two we learned that the two exceptional sacrifices that are disqualified if offered with the wrong intent are the pesah and the hatat. All other sacrifices are valid if slaughtered with the intent of their being different sacrifices. Rabbi Shimon ben Azzai quotes this tradition as being true only for sacrifices that are eaten. This would not include the olah, which is wholly burnt. According to ben Azzais tradition, the olah is disqualified if it is slaughtered with the intent of it being a different sacrifice. The final line of the mishnah notes that ben Azzai added the olah to the pesah and hatat, but that the sages (whose opinion is found in mishnah one) did not agree with this tradition.
Rabbi Shimon Ben Azzai states that he received this tradition on the day that Rabbi Elazar ben Azariah was appointed a member of the yeshiva (academy). This seems to be a famous day in rabbinic recollection and there is a significant amount of aggadah concerning the background to this appointment. The most expansive version of this aggadah is found in Bavli Berakhot 27b, where Rabbi Elazar ben Azaryah is appointed head of the academy after Rabban Gamaliel is deposed. The historical accuracy of that legendary account is a bit suspect, but here in the Mishnah we can see that although we might not know exactly what happened that day, it was a memorable day, one which later rabbis used as a reference point.