Gemara

(Mishnah): A Kohen comes before Levi, a Levi before a Yisrael...

This is when they are equal in Chachmah. A Mamzer Chacham precedes a Kohen Gadol Am ha'Aretz (ignoramus).

Chulin 130b (Beraisa): "V'Zeh Yihyeh Mishpat ha'Kohanim" teaches that Beis Din enforces the Matanos (when a Chulin Behemah is slaughtered, the foreleg, jaw, and stomach are given to a Kohen).

Suggestion: This means that Beis Din makes one pay for damaging them!

Answer: No. Beis Din forces a Yisrael to give the Matanos to a learned Kohen;

(Rav Shmuel bar Nachmani): We do not give Matanos to a Kohen Am ha'Aretz - "Lema'an Yechezku b'Soras Hash-m".

Menachos 53a - Rabanan: R. Ezra descends from R. Elazar ben Azaryah and from Ezra!

Rav Freida: If he is a Chacham of good lineage, that is great. If he descends from Chachamim but is not a Chacham, fire should consume him!

Megilah 28a: One merit to which R. Freida attributed his long life was that he never blessed (at a meal) before a Kohen.

Question: R. Yochanan taught that if a Chacham allows a Kohen Am ha'Aretz, even a Kohen Gadol, to bless before him, he is worthy of death! We read "Kol Mesan'ai Ohavu Maves" like 'Masni'ai' (those who make people hate Torah).

Answer: R. Freida never blessed before a Kohen Chacham.

Rishonim

The Rif and Rosh (Berachos 35a and 7:19) bring the Gemara in Megilah.

Sefer ha'Mitzvos (Aseh 32): We are commanded to honor the seed of Aharon, to elevate them and put them first and foremost. "V'Hayu Kodesh" includes even a blemished Kohen.

Rambam (Hilchos Klei ha'Mikdash 4:1): It is a Mitzvas Aseh to separate the Kohanim, be Mekadesh them and prepare them to (offer a) Korban - "v'Kidashto Ki Es Lechem Elokecha Hu Makriv."

Minchas Chinuch (269 DH v'Hinei ha'Rav): This implies that one need not honor a Ba'al Mum, who cannot serve. This is unlike the Sifra!

Minchas Yitzchak: The Rambam relies on what he wrote in Sefer ha'Mitzvos.

Rambam (Hilchos Matanos Aniyim 8:18): A Kohen comes before a Yisrael when they are equal in Chachmah. A Mamzer Chacham comes before a Kohen Gadol Am ha'Aretz.

Rosh (Megilah 3:19): A Ba'al Mum may Duchan unless he has a Mum on his hands that people will look at. All the more so he reads first in the Torah.

Rivash (94): If a Kohen does not conduct with Kedushas Kehunah, he forfeits the Kedushah. Similarly, we do not give Matanos to a Kohen Am ha'Aretz (Chulin 130b). A Mishnah in Chalah says that Matanos are given to any Kohen. Some say that this refers to a Kohen in any Mishmar. The Ramban says that it refers to even an Am ha'Aretz. Chulin 130b forbids to an Am ha'Aretz only when a Chacham Kohen is around. Even the Ramban would not require punishing greatly one who disgraces a Kohen Am ha'Aretz, for the Kohen does not learn Torah like a Kohen should. Chachamim did not refrain from cursing Kohanim of the greatest lineage who acted improperly (Menachos 53b, Yoma 71b). All the more so this applies nowadays, when Kohanim cannot prove their lineage.

Mishneh l'Melech (Hilchos Kinyan 3:8): We may learn from the Rivash that one may use an Am ha'Aretz Kohen. Perhaps such a Kohen may be sold.

Shirei Berachah (4): The Rif, Rambam and Rosh did not bring the law that we do not give Matanos to a Kohen Am ha'Aretz. They hold that it is only a preference, like Perush ha'Mishnayos (Sof Chalah). I hold that the Isur to use a Kohen applies even to an Am ha'Aretz. However, a Talmid, even a Kohen, should serve his Rebbi. This explain why Rav Chisda served Rami bar Chama before learning a Halachah from him (Bava Kama 20b)

Minchas Chinuch (269 DH v'Ayen): Perhaps only a Chacham is exempt from honoring a Kohen Am ha'Aretz.

Poskim

Rema (OC 167:14): If one of the people who will eat is a Kohen, it is a Mitzvah to give him precedence (to bless). If he is an Am ha'Aretz, a Chacham comes first. If the Kohen is also a Chacham but a smaller Chacham, it is good, but not obligatory, to put him first.

Magen Avraham (31): One who puts a Chacham Kohen first will live long.

Shulchan Aruch (201:2): A Yisrael Chacham may not tell a Kohen Am ha'Aretz to bless first due to his Kehunah. He may permit the Kohen to bless first. It is a Mitzvah to give precedence to a Kohen Chacham to begin and bless first - v'Kidashto.

Source (Mordechai Megilah 828, cited in Beis Yosef DH v'Chosav).

Mishnah Berurah (11): If neither is a Chacham, the Kohen is first.

Magen Avraham (282:6): Some say that if the only Kohen is a minor, we call him to read first from the Torah. I say that v'Kidashto does not apply to a minor. "Lechem Elokecha Hu Makriv" does not apply to him.

Question (R. Akiva Eiger and Minchas Chinuch): The Sifra applies v'Kidashto to a Ba'al Mum, even though he cannot serve!

Answer (Hagahos Har Tzvi, in Minchas Chinuch): A minor is allowed to eat Kodshim, but he has no Mitzvah to eat Kodshim, unlike a Ba'al Mum.

Nish'al David (OC 4 DH Ach): We may learn from this that v'Kidashto does not apply to a Ba'al Mum, either.

Kaf ha'Chayim (128:281): The Kesav Sofer (15) proves that v'Kidashto applies to a minor or a Ba'al Mum. One should be stringent.

Aruch ha'Shulchan (128:72): It is not clear whether or not a Kohen must honor another Kohen. It seems that one may use a Kohen Ba'al Mum.

Shulchan Aruch (YD 251:9): If there is not enough Tzedakah for all the poor, the order of preference is Kohen, Levi... This is when they are equal in Chachmah. A Mamzer Chacham comes before a Kohen Gadol Am ha'Aretz.

Shach (246:14, citing Be'er Sheva): v'Kidashto is only when there is no Chacham greater than the Kohen. If the Yisrael is a greater Chacham than the Kohen, it is good for him to put the Kohen first, like R. Freida did. If the Kohen is an Am ha'Aretz, it is forbidden to put him first due to Kehunah, but one may allow him to bless. A Kohen Chacham may permit a Yisrael who is a lesser Chacham to bless. We forbid this only for Kri'as ha'Torah.

Magen Avraham (128:7): If all the Kohanim are Amei ha'Aretz, a Levi Chacham need not wash them (for Birkas Kohanim). Some disagree. If at least one Kohen is a Chacham, all agree that the Levi must wash all of them.