In the scenes with Paul Newman in her apartment early in their love affair, Piper Laurie's lines as Sarah are overdubbed. You can hear an audible dead spot in the soundtrack just before and after Paul Newman's Fast Eddie responds to her lines. Clearly a post-production issue and a distracting aspect of Laurie's performance in the film.
During the last match between Fats and Eddie, in the first game, Fats attempts a soft break, leaving the cue ball against the rail. In the establishing shot, the cue ball is clearly bouncing away from the rail, in the next shot, the ball is tight frozen against the rail.
During the last pool match, second game, Minnesota Fats has taken his jacket off, loosened his tie and unbuttoned his vest, but one subsequent shot shows him with his tie tightened and wearing a buttoned vest and jacket.
When Eddie puts on his coat and calls Fats "beautiful", his coat collar is turned under. He turns around while laughing, and when he turns back to face the camera, his coat collar is out, in its proper position.
In the last game with Fats, Eddie starts by calling and pocketing the 1 ball and the 12 ball. Eddie is talking to Bert as he sets up his next shot, a 4 ball, which he then pockets. His next string of calls - the 5 ball, the 14 ball, and then the 4 ball again (which he had already pocketed).
During the last game, Eddie calls and pockets the 1 ball. Then he sets up, calls the 12 ball and you hear the ball dropping into the pocket. Eddie then walks around to the other side of the table and calls the next shot - the 12 ball again.
When Sarah walks into the bathroom, we see Bert Gordon in the mirror. Then when Eddie walks into the bathroom and sees Sarah on the floor, the sink and mirror have been moved to the left side of the room.
The first time we see Eddie play, he tries to duplicate the corner shot the second time but misses. The chalk and wallet next to him disappear when he takes the shot, but return in different positions as the ball rolls off the table.
After thugs break his thumbs, Eddie wears cast on his hands that remain sparking white for weeks - an impossibility because casts are dirt magnets that quickly become dingy-looking under the best of conditions and he's seen spilling coffee on them, lives in a seedy apartment, goes outside for a picnic and so on.