1. On Shabbos, one may remove by hand a blemish from an animal designated as a Korban.
2. One may not cut off the blemish with a knife, even in the Beis ha'Mikdash.
3. The Gemara explains why the Chachamim allow people to start roasting the Korban Pesach close to the onset of Pesach which falls on Shabbos.
4. If a Kohen has a blemish, he or his friend may bite it off with his teeth.
5. A Kohen may apply a medicinal bandage when he is serving in the Beis ha'Mikdash.
A BIT MORE
1. This is because doing so with one's hand instead of with a knife is prohibited only mid'Rabanan, and Isurim d'Rabanan are generally suspended in the Beis ha'Mikdash.
2. Some say that if the blemish has dried up, then one may cut if off with a knife.
3. Although the Chachamim prohibited placing a raw item on the fire to cook just before Shabbos lest one stoke the coals on Shabbos, they were lenient with regard to the Korban Pesach because the people preparing the Korban Pesach are knowledgeable and careful not to sin.
4. This is similar to the law above (#1) regarding a Korban.
5. Even though the Rabanan prohibited using medicine on Shabbos to merely alleviate pain, it is permitted in the Beis ha'Mikdash in order to help the Kohen perform the Avodah in an honorable manner (see #1 above).