Continuity mistake: When Mike first enters room 1408, there are three light switches on the wall. He flicks on two of them. A few seconds later, you see the switches behind him, but it is two different switches that have been flicked.
Continuity mistake: When Mike is speaking with Olin the first time, Olin has a handkerchief in his chest pocket, and two 'points' stick out. But after Olin tells Mike that he thought the "father was a bastard", there are three points sticking out for the rest of the conversation, even through the elevator ride.
Continuity mistake: As Mike scrolls through the microfilm, we see his view as the pages scroll from right to left. The shot then reverses to show his face through the scrolling film, but while the film is now properly reversed, it's still moving right to left in our view. But this reversed angle should show it moving left to right.
Continuity mistake: After slamming his hand in the window, Mike bangs on the front door leaving blood on the left side of the map on the door. Later in the film, there is blood on both sides.
Continuity mistake: When Mike is in the room holding his crying daughter, the blood trails from his nose and ears change constantly between shots.
Continuity mistake: At the hotel in the beginning during the rainstorm, you can see a gap on the road of where rain isn't falling as well as where it stops in the distance. Once Mike's truck comes to a stop, the camera angle changes and the "rain" gap is gone.
Continuity mistake: When Mike steps off the elevator, he is between the elevator doors and a dark statue in the middle of the hallway. The statue is seen behind him, slightly to our right. When the elevator doors close, Mike's location is different as he begins to walk down the hall. Relevant to the earlier shot, he is much further to our right and farther from the elevator doors, as now has to walk around and past the statue he was originally already past.