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: When Eddie talks to Carmen in the motel room, Carmen looks at Eddie to talk him, but when the scene cuts, she is suddenly watching the television. Since it's a straight cut, there is no time for her to move her head. (00:51:25)
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)
Factual error: While getting hustled by Amos, Fast Eddie wins a game on a 6-9 kick combination. But, the 3-ball is on the table near it. Can't play the 6-ball if a lower numbered ball is on the table in the game of 9-ball. (01:19:00)
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)
Other mistake: When Eddie sees himself reflected in the ball, his reflection is not reversed. (01:46:30)
Other mistake: When Eddie arrives at the casino, a man with a white jacket can't help staring at the camera for several seconds.
Continuity mistake: During the trio's first dinner, Carmen's right arm is visible behind Vincent's back. Then she moves it away, grabs a cigarette, and places her arm and hand behind his back again. In the following shots, her arm is not visible.
Visible crew/equipment: During the second trip around cities, the camera is very close to the car, and a rectangular black object is reflected on the chromed frame of the grille, most surely the camera or the structure it was attached to. One can see what seems to be fingertips on the upper part.
Continuity mistake: When all three are having dinner for the first time, Vincent's hands' positions are not continuous between shots. Sometimes they swap between crossed or not, or they're holding a glass or not, or the glass swaps hands.
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.
Answer: Because it wasn't about the money or a personal issue with Vincent. Eddie had a sudden realization about his own integrity and what he was doing (helping to rig games' outcome to skew betting odds). He wanted to win legitimately against Vincent. Earlier, he had become rather fed up with Vincent's egotistical nature and arrogance, which led to them parting ways.
raywest ★