Plot hole: Jude kills his victims by biting their necks and drinking their blood - the wounds should be quite obvious, yet the coroners don't appear to have noticed them.

Other: When Jude Law and the police officer are walking to the officer's car, Jude asks the officer if he is married. Why is it he asks this? Earlier on in the film, at the police station, the officer told Jude that his wife gave him that very same necklace.