(at around 16 mins) When Rivers first encounters Price, Price places his business card atop a circular-shaped thing in the doorway of the building. After a shot of Rivers and Price, the card disappears. Price walks away, we cut back to Rivers and the card reappears on the wall.
(at around 52 mins) When Mike is flipping through the channels on television, he stops on a news report about Mary Freeman. After a close up of Mike's face, the next shot shows cartoons on television but we still hear the voice of the reporter for a second before we hear the sound of him changing the channel to cartoons.
(at around 1h 2 mins) When John is at Carol Black's funeral, he stops to Carol Black's husband. A bald man with dark rimmed glasses walks past them to exit the church, and takes an obvious look at Carol Black's husband. The camera then focuses on John for a couple seconds. When the camera again focuses on Carol Black's husband, the same bald man with dark rimmed glasses walks past them to exit the church.
The goof item below may give away important plot points.
When Jonathan first meets Raymond Price, he tells him that the voices and visuals are not "live", you have to record and then listen to the playback. But at the end of the film, when Jonathan's ex-wife is sitting in the car with his young son, you hear the voice come over the static radio - this was therefore live and not a recording.