Continuity mistake: On the airplane, Rock Hudson takes a pillow from the stewardess, and puts it behind his head. They cut away to the stewardess, and back to Hudson, and the pillow is gone. They cut to the stewardess again, then back to Hudson, and the pillow reappears.
Continuity mistake: When the German agents dig up Gromek's buried motorcycle and are pulling it out of the hole in the ground, it is completely clean and in perfect condition with no dirt, scratches, or dents on it.