Factual error: When Angelus is torturing Giles in this episode he is seen with Giles' glasses, and he cleans them by breathing on the glass and wiping with a cloth. Vampires don't have breath, as Angel tells Xander in 'Prophecy Girl' from season one - even if he can force some air out of his body, it wouldn't be warm, moist air, which is needed for condensation to clean glasses with.
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.
Revealing mistake: Towards the end when Oz says to Veruca, "You don't wanna find out what I am", and partially turns into a Werewolf. You can tell that both of the actors were filmed separately for the CGI's sake as Oz stands out from the picture more than Veruca does. The same effect is obvious during "Doppelgangland" in season 3 where there are 2 Willows onscreen at once.
Continuity mistake: In the very last episode, Chosen, in the shot right before Spike's amulet sends out the blast through the roof, you can see an ubervamp just about to pin him against the wall and in the next shot he is standing in the middle of the area backing up toward the stairs and then he sends out the blast. There would never be enough time between the shots for Spike to break free and then go and stand in the middle of the floor.