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Continuity: When Brittany Murphy writes down the number on the glass she writes it backwards because that's how she sees it in her mind. Watch closely, though, and you'll see a perfectly normal 2 which isn't written as a mirror image of 5. Later, when Michael Douglas realizes this catch, he looks at the piece of glass again, this time from the other side, and the 2 has turned into a 5, which apparently was written in a different style.
Continuity: When Jennifer Esposito is talking to the morgue doctor, when looking at some dead bodies, he asks for a look at the police file, which Esposito had been looking at herself, and so was open. The next shot, which actually shows Esposito passing the file to the doctor, shows that the file is now closed.
Continuity: When Dr. Conrad meets Elizabeth Burrows for the first time in the mental hospital, she is sitting catatonically on the bed. She is sitting bolt-upright with a very straight back. As the doctor walks by her, she is shot from the front and now she is slumped forward with her shoulders down. In the next shot, she is sitting with her back straight again.