Continuity mistake: In the season one finale "To Shanshu in LA," near the end Angel is fighting Vocah in the mausoleum and Angel rips off Vocah's mask, revealing the maggoty face Underneath. In subsequent shots of Angel from behind Vocah, you can still see the edges of the mask on his face. (00:34:30)
Continuity mistake: When Faith is sitting at the window and looks at the piece of broken glass she used to torture Wesley, it has a different shape than the one she first takes to torture Wesley. When she drops it out the window it has its original shape again. (00:33:10)
Character mistake: When the bidding for Cordelia in the auction reaches $20,000, somebody bids for $30,000 after the auctioneer has said "going once, going twice" and they end up winning. The auctioneer should have in fact restarted saying "going once, going twice" after the $30,000 bid was made.
Character mistake: Angel comments that Vanessa was acquitted because of a hung jury. A hung jury means the jury couldn't come to a unanimous decision; the case would require a new trial, while an acquittal means the jury found her not guilty, and she couldn't be tried again for the crime.
Revealing mistake: At the vampires' nest, when Knox is talking about Gunn's team, the vampire wearing the green sweatshirt and leather vest doesn't have yellow eyes like the other vampires do. And the female vampire doesn't either later, when the two groups face off after Gunn's sister is sired. (00:22:30 - 00:35:35)