Importance of citing the correct source, for purposes of determining self-contradiction and argument: Pesachim 107a
Importance of mentioning that a source is Biblical: Gittin 4a
Citing a source with its statement brings the Redemption to this world: Megillah 15a; Niddah 19b
Value of having learning said over in one's own name: Pesachim 104b
Making sure to tell over a Law from the original source: Pesachim 52b; Moed Katan 24b; Chagigah 3b
Citing a law, and not only that the law is like X, to prevent error: Megillah 31b-32a, 32a; Gittin 28a
Citing a law from Sage X in the name of Sage Y, and then stating that it is unclear whether it was Sage X's opinion or only that of his teacher, Sage Y: Niddah 10b
Levi cited a ruling from Rebbe, and nobody listened, but then he cited it as being a majority view and it was approved: Gittin 20a
Talmud asking why a Baraita bothered to mention an extra authority: Shabbat 145b
Reversing the attributions [Eipoch / Muchlefet haShitah] in a Mishnah to match known views of the Sages of the Mishnah involved: Shabbat 143a; Eruvin 37b, 38b; Beitzah 3a-b; Temurah 27a-b
Reversing attributions to fit whichever side has a greater number of sources: Eruvin 37b Shemuel changing the sides of a debate when retelling it, so that people would hold like Rebbe in it against the majority opinion: Pesachim 27a
Rabbah making a statement in the name of R' Yosi to Rav Yosef, not because R' Yosi actually said it, but because that way Rav Yosef would accept it: Eruvin 51a Rava reversing the sides in a Mishnah to match known views of the Mishnaic Sages involved: Bava Metzia 7b Rabbah quoting a prohibition from R' Yochanan, although it wasn't so, so that it would be accepted: Shabbat 115a
Backing an Established Source with an Unestablished Source ["Tali Tanya BeDiLo Tanya"]: Ketuvot 2a
Backing an Explained Source with an Unexplained Source ["Tali Tanya DeMifaresh Taama BeTanya Delo Mefaresh Taama"]: Ketuvot 2a
When an anonymous "student" cites R' Yishmael in front of R' Akiva, that student is R' Meir: Eruvin 13a
2 Sages of the Mishnah Arguing in the Meaning of the Words of... [Trei Tannai Aliba de...]
