King Yoshiyahu hiding Aharon's staff: Yoma 52b; Keritot 5b
Aharon's response to Moses, explaining why he had allowed the creation of the Golden Calf: Megillah 25b
Whether Aharon contracted tzaraat along with Miriam: Shabbat 97a
Moshe and Aharon acting as the first court for declaring the New Month: Rosh HaShanah 25b
Gideon, Yiftach and Samson are known as the 3 "world lightweights," but their judicial power for their generation is compared to that of Moshe, Aharon and Samuel, the "world heavyweights": Rosh HaShanah 25a-b
Moses learned from Gd. Moses then taught it to Aharon, and Aharon sat by his side. Moses then taught it to Aharon's two sons, who then sat by their side. Moses then taught it to the elders. Moses then left, and Aharon taught it to the others. Aharon left, and his sons taught it to the others. The sons left, and the elders taught it to each other. This way, each learned four times: Eruvin 54
The two drops of oil which remained on Aharon's beard from the time he was anointed: Keritot 5b
The concerns of Moshe and Aharon that they may have trespassed because of the two drops of oil of anointment that remained on Aharon's beard, and Gd's answer: Keritot 5b
Aharon's exclusion from the census of the tribe of Levi in Bamidbar 3, when they redeemed the first-born, as represented by dots over his name in Bamidbar 3:39: Bechorot 4a
Elazar, Aharon's son
Elazar lost his position of greatness because he ruled in law before Moshe, even though he worded his statement "Gd told this to my uncle." This is why Yehoshua never is mentioned as having needed Elazar's help: Eruvin 63a