Factual error: Cruise is breaking and if you watch the eight ball after the break it's following the 5 into a pocket at the end of the table closest to Tom. Now the 8 ball didn't necessarily go in because they focus on the one ball, but in the next frame shot, there's no way it could be at the opposite end of the table like they show. (00:29:20)
Continuity mistake: At the very start of the tournament, when we see all the platters break at the same time (wide shot showing all tables), we see Eddie's table is second from the left and three tables up. Notice the referee one table behind Eddie. In the close shot after the break, we now see that the referee, who was standing still in the wide shot, is now a table further down.
Revealing mistake: When Paul Newman is playing in the tournament near the end after Tom Cruise humiliates him by dumping the game, Newman lines up to shoot the 2 ball. The point of view shot shows his detailed reflection on the ball's surface. If you look closely at the bottom right side of the ball, you can see that the "reflection" of his shirt exceeds the outside boundary of the ball.
Continuity mistake: When Vince starts to play Moselle he still has the injury on his lip. As soon as they're done and Vince leaves with Eddie his face is completely healed. (00:53:37)
Continuity mistake: Eddie tells Vince and Carmen that they should go it alone to Atlantic City but Vince and Carmen try to reason with Eddie in the stairs leading up to the pool hall. Eventually, Vince gives in and then demands money from Eddie. However, Vince then decides he no longer wants the money and so rips the hand rail off the wall and then goes back up to the pool hall, leaving Carmen and Eddie in the stairway. When Vince leaves you can see that the hand rail is lying on the floor but when Carmen finally accepts money from Eddie you can see that the hand rail is attached to the wall again. (01:21:45 - 01:22:45)