When Aiden confronts Mr. Spitz about the pictures with Kristin, he is holding up a picture with just Kristin in it. The camera changes to Mr. Spitz then back to Aiden in which he is holding up a different picture, however his hands did not move.
In the scene where Detective R. Rodriguez (Clifton Collins Jr.) is reading "the great day of his wrath has come" from his monitor to Detective A. Breslin (both are seating at their desks), Breslin's monitor is off, yet a few seconds later you can see someone's AIM buddy list on it.
In the beginning of the movie, when the Detective visits the second dead body of the girl, you can see the detective going to talk to the daughters, but in the next shot when their father comes in, the detective is standing next to the policeman again, and then returns to his original position in the next frame.
(at around 1 min) The main character runs into the bathroom, fills the sink with water, and puts his head in it. With the underwater camera you see he gets his hair wet but when he pulls his head out of the water his hair is dry.
Where this is supposed to take place in Detroit, when driving through the city at night about 20 minutes into the movie you can clearly see "The Bay" (Canadian department store) and "Rogers" (Canadian telecommunication company) signage.
The goof item below may give away important plot points.
Crew or equipment visible
When Det. Breslin and Kristin are walking prior to her confessing to him, it is so cold that their breath can be seen. When the camera is directly in front of them, you can also see the breath of the cameraman pass in front of them several times.