John finds the 'Black and Tan' magazine at a newsstand. The salesman looks right into the camera and clearly has nothing in his mouth. In the very next shot, the magazine salesman is reading and has a cigar in his mouth.
When Horton, after meeting the PhD student, opens his wallet to pay in the diner, something falls out of it near the counter. No one notices or refers to it.
When he's playing the piano, James Whitmore never changes the movement of his arms as the song changes.
James Whitmore was a consummate character actor, yet he never bothers to adopt a black, or even southern accent to enable his character to pass.