Character mistake: When Faith arrives in LA she is carrying a bag. She puts it on the ground and then steals a man's jacket and wallet. Afterwards however, she leaves without picking up her bag.
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.
Blind Date - S1-E21
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.
Answer: Everybody including Angel saw her. After helping them and then being left alone to talk to Angel, Cordelia says that the Powers That Be let her come back one more time to help them. After Angel gets a call saying that she died, he realises that it was her spirit that was helping them the entire time.