Revealing mistake: When Buffy is fighting the vampires that are trying to resurrect The Master, at one point she is grabbed from behind by a male vampire and kicks a female vampire in a green top twice (right after Absalom shouts "The sacrifices! Stop them!"). If you watch closely, both of the kicks miss the vampire, revealing that the fight was choreographed. The punch that she delivers to the male vampire afterwards also looks fake.
Continuity mistake: When Buffy and Spike are fighting on campus during the day, Xander tries to help Buffy but Spike throws him against a lamppost. When he lands in the ground he falls completely on the grass on his side but if you look behind Spike in the next shot he lies half on and half on the grass on his front.
Continuity mistake: In 'Consequences' Buffy says to Faith 'Less that 24 hours ago you killed a man'. In 'Bad Girls', Faith kills Finch in the alley on the first night. One night later Buffy and Angel are attacking Belthazor, the night after that is the night when Buffy dreams about drowning, so the night when Buffy says this is actually about 72 hours after the murder.
Audio problem: In the episode 'Once More, With Feeling', when Anya sings her first few lines of the song 'I'll Never Tell', you can still hear Xander talking about omelettes in the background, but for the last few lines he speaks (from 'I could do an omelette' onwards) you can see over her shoulder that his voice is dubbed.
Plot hole: When Buffy and Sheila are walking out of school after the meeting with Snyder, Xander runs up to talk to them. He mentions during this scene how Buffy will be helping out at the Parent-Teacher Night, but he shouldn't know this - Buffy only just found out about it in the meeting with Snyder.