When Det. Dowling "borrows" the book from Prof. Lattimore, the chalkboard eraser is laying on the desk. Then Prof. Lattimore is rubbing the desk with it. Then it is stationary again, before disappearing altogether in the long shot.
At the beginning of the movie, when Charles talks with the student in front of the university building, his tie goes from loose to neatly tied between shots.
In a class scene, Pierce Brosnan's character writes the word "motive" on the blackboard. He writes the word across the entirety of the blackboard, using one continuous motion to write the letter "o" and underlining it four times. Later in the same scene, the word only encompasses a smaller portion of the board, and it is clear that the letter "o" was written using two separate motions, and the fourth underline is much longer.
In the scene in Charles' classroom with the detective (where the detective borrows the book 'The Big Sleep'), the desk goes from chalk covered to perfectly clean several times.
When Charlie calls Mike on the phone, Mike's wife can be seen sleeping next to him. Her uncovered face is briefly visible during the first moments of the phone call. When Mike turns around turns around after the call has ended, we can again briefly see his wife's face, but this time she's wearing a sleeping mask, though she's in the very same position as before and hasn't made any visible movements to put it on.
At the beginning of the movie, when Charles talks with the student in front of the university building, a studio light is clearly seen to the left.