Continuity mistake: There is a scene during the cops' frantic search for the first missing girl where a red-headed lady cop is sitting at a desk with a computer screen. On the screen, however, is the picture of the SECOND girl, not the first one. The picture of the second girl hasn't even been sent to them yet.
Continuity mistake: When two cops let themselves into Spader's apartment, as they approach the door you can see that the door has an old style lock, sometimes called a lever lock. As they go to pick open the lock the close-up shows a different lock, a pin type deadbolt on a different color metal plate. When the door opens it is back to the lever type lock and a shiny metal plate.
Factual error: When the police are looking at the reflection of a neon sign in the glasses in the picture of the girl, the letters are reversed as you might expect. But the sign is on the glass front wall of the shop, facing the outside. Since the photo was taken inside the shop, the inside view of that sign would have already been reversed, and the reflection should have been the right way round.