The burn on J.B.'s hand is only visible when Petersen notices it. It disappears in every other scene where his hand is visible (like when he is sitting on the couch with Dr. Brulov).
When Dr. Petersen enters the library at the mental hospital, the word "LIBRARY" is clearly visible on the door in large letters. When she exits, it is gone.
During one of the sessions, everyone notices it is snowing outside. Out the window, a child lying on his stomach goes down the hill on his sled. The camera cuts back to the people in the room (who are talking about the white snow with the dark track marks), then back at the window again. The same child, on his stomach, goes by on his sled again, even though he would not have had enough time to climb back up the hill.
In his first scene Dr. Brulov's hair changes.
Right before Dr. Petersen gets a letter from Dr. Edwardes, she cleans her glasses on her coat and the position of her hands varies between shots.
When John Ballantyne, after seeing snow in Dr. Brulov's house, drops and breaks a cup full of coffee, no coffee spills on the carpet. Instead, we see some thin black disc made from wood or plastic pasted into the cup.
When the hotel bellboy brings the newspaper to Constance he notices her photograph on the front page. Freeze-framing reveals that the articles adjacent to the photograph are actually random paragraphs of text.
At approximately the 25 minute mark, when the doors open by themselves, a crew member's arm or a long pole can be seen through the crack between the door and the jamb. Whatever it is, it appears to be pulling on something narrow hooked to the door knob, as it doesn't give the appearance of there being a hand grabbing the door knob.
When Lieutenant Cooley ends his phone conversation with "goodbye" (in his first scene in the film), the telephone receiver is not only not near his mouth, it's almost back in the cradle.