Revealing mistake: The "hand" holding the gun rotates 180 degrees while the shooter's point of view does not move. A real hand can't reproduce that motion without moving extremely close to the face.
Continuity mistake: In the scene preceding Emily Brent's death, Judge Francis J. Quincannon moves his glasses around, creating a couple of obvious discontinuities, first when his hands from distanced become joined at the very beginning, and then at the bottom of the stairs when he waves Blore to stay put. (00:58:50)
Continuity mistake: The policeman drives up to the house and parks his motorcycle facing the front door. He goes to the door to talk and then returns to his motorcycle and prepares to leave. When he gets back to the motorcycle, it is now parked facing away from the door. (00:08:05)
Continuity mistake: Doctor Leo sits at the desk and begins writing a letter to Alec Ritchfield. "My dear Alec", it starts. Fade to the finished letter, but you can easily tell that it's not the same letter, the handwriting being different - look at the little flourish below the M, not to mention the position of the text in relation with the Fog Island stamp. (00:08:25)
Continuity mistake: After the scene with Junior that busted him as the night kitchen raider, Dick is in his office. Pat Patton tells him about his findings going through the victim's belongings. He leans forward with his left arm, and Dick at the same time pulls his own arm back away from the desk. Next cut and Dick has both hands on the desk and Pat just his right arm on it. (00:12:35)