Corrected entry: In 'Faith, Hope And Trick', Kakistos and the other vampires enter Faith's apartment without an invite.
Corrected entry: When Buffy complains about Faith's methods, Giles reminds her "She did kill one of them in the alley", but during the alley fight Faith didn't kill anyone. Buffy staked all four vampires.
Correction: He was talking about the one Faith killed earlier outside the Bronze, when Buffy first met her.
Corrected entry: When Faith asks Buffy what her toughest kill was, she tells her "The Three", from the season one episode "Angel", but in that episode Buffy barely encountered them. She saw them once in an alley and was barely harmed in the encounter - in the end, it was Darla who killed them. One would assume her first thoughts would be of someone like the Master (who killed her) or The Judge (who was indestructible).
Correction: Buffy is distracted because she is thinking about her actual toughest kill: Angel. She mentally grasps for some fight that was not witnessed by anyone present (who might contradict its difficulty) and comes up with the Three. Neither fight with the Master lasted more than a few minutes and the Judge was killed in one hit from a rocket launcher.
Correction: Faith lives in a motel. Public accommodations are an exception to the invitation rule.
Captain Defenestrator