Menachos 3:2-3

Menachos 3:2

If the kohein didn’t pour in the oil, mix it, break the offering into pieces, salt it, wave it or bring it near, or if he broke it into large pieces, or if he didn’t anoint it, it remains valid. If the handful of one flour offering got mixed with the handful of another flour offering, or with a kohein’s flour offering, or with the flour offering of the Kohein Gadol, or with the flour offerings that are offered with libations (i.e., accompanying animal sacrifices), it is valid. Rabbi Yehuda says that if the handful got mixed with the flour offering of the Kohein Gadol or with one that is offered with libations, it is invalid. This is because the former is of a thick consistency and the latter is of a thin consistency, so they absorb from one another.

Menachos 3:3

Let’s say that two flour offerings whose handfuls had not yet been taken got mixed together. If it is still possible to take the handful from each of them individually, they remain valid, otherwise they are invalid. If a handful got mixed with a flour offering from which the handful had not yet been taken, it is not burned. If it was burned, then the flour offering from which the handful was taken fulfills its owner's obligation; the other offering, from which the handful had not been taken, does not fulfill its owner’s obligation. If a handful got mixed with the remainder of its flour offering or with the remainder of a different flour offering, it is not burned. If it was burned, it fulfills its owner’s obligation. If a handful was rendered ritually unclean but it got offered anyway, the tzitz (the Kohein Gadol’s head plate) atones for it (causing it to be accepted). If it was taken out of the Temple courtyard and subsequently offered, the tzitz does not atone for it (so the offering is not accepted, not even post facto). This is because the tzitz only atones for offerings that were rendered ritually unclean, not for those that got taken outside.