Other mistake: When Alice asks Dan to make her some tea (after he tells her about him and Anna), he walks into the kitchen for just a moment, and comes back to find her gone. He also doesn't see her as he runs downstairs and looks outside. She couldn't have quietly gone down the stairs and out of the building in the short moment that Dan was in the kitchen. If she had moved quickly, there should have been a lot noise from her footsteps.
Factual error: When Julia Roberts takes a photo of Natalie Portman crying she uses a 35mm camera. The final photo in the gallery is from a Hasselblad type camera shooting a square format. All the prints show the full negative and the outside area of the negative. Also when she uses the 35mm camera sometimes she advances the film manually and sometimes you hear a motor drive. It would be either one or the other. Last she doesn't focus the lens when she takes a picture.
Continuity mistake: When Dan is in Larry's office, the bed behind Dan has tissue paper protecting it. After Larry gets up from behind his desk he goes up to Dan. Larry then goes to the bed and pulls a paper sheet over the uncovered bed to ready it for his next patient. Larry was never near the bed in any of the shots before this and even the one rare shot he was not on camera he wouldn't have had time to remove the sheet and get it out of the way.
Continuity mistake: When Clive Owen throws most of the money at Natalie Portman a bit after he keeps trying to find out her real name, she is putting the money into her handbag. As she is putting the money in her handbag she is holding it up near her chest. The following shot she is still putting the money in her handbag but it is now close to or resting on her legs.