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.
Character mistake: While Gunn and Lorne are interrogating Framkin he sings a couple bars of a song "Courage and Pluck". However, though he has the ability to read people when they sing, and in fact in the very next episode knows that Fred is about to fall from just the words "you make me happy", Lorne doesn't read him.