Monster throws a dart into the front of Rudy's shoulder, but in the next shot it is stuck in the back of his shoulder (shots of additional darts being thrown were cut from the final version so we never see this one land).
When Rudy finally gets to eat his pecan pie, we see him eat the last piece, but in the next shot there are still pieces of pie on the plate.
When Rudy is pointing the water pistol at one of the gang members, at one angle, his arm is fully extended. At a different angle, his elbow is bent so we can see the gun as his face in the same shot. When they cut back and forth, Rudy's arm jumps from extended to bent and back.
When Rudy is pulled out from under the ice his jacket jumps from being buttoned to unbuttoned between cuts.
In the pool scene with Gary Sinise and Charlize Theron, Charlize glass changes hands between takes.
While escaping across the ice alone, Rudy gets shot at, and despite being in the middle of a frozen lake, with nothing for a distance on either side, a bullet ricocheting off metal can be heard right next to him.
Rudy is given a bottle of rum before the robbery. The bottle says it's Bacardi Light rum, which is clear, but the liquid in the bottle is brown, the color of dark rum.
When the gang are in the casino dressed up as Santa Claus' one of them puts their drink down on the casino table. This is a major no-no in all casinos which for some reason is not flagged up by any of the staff.
After being submerged in ice water, in addition to being in freezing weather, there is no way that Ashley and Rudy wouldn't have gotten hypothermia, or even just freeze to death. Afterward, they were shown to be just very cold. They weren't even taken to get any medical treatment.
When Rudy (Ben Affleck) is trying to hot wire the car you can see the ignition is in the "on" position. Plus the car could not be taken out of "park" without the key being unlocked.
When the gang initially robs the casino, they are telling the security guards to drop their guns. One of the guards has the gun up and ready, but the slide is obviously back. There is no way the security guard could have shot the gun with his gun not ready.
Early in the robbery scene, before any shots are fired, one security guard's gun has its slide locked back, as he points it at the Santas.
When questioning Rudy about his true identity, and how much he knows about Ashley's background, Gabriel puts a Glock to Rudy's head. Upon doing so, it sounds like a hammer cocking back on the pistol. Glock pistols do not have hammers.
During the reconnaissance of the Tomahawk, the college kid says, "He gave me a hundred bucks!" and his mouth doesn't move at all.
In the first scene at the Tomahawk Casino, "Nick" bumps into a waitress and she drops the drink she's carrying. A glass breaking sound is heard. Also when one of the characters discovers that there was no remodel done on the Tomahawk - he runs off, dropping his glass - and the sound is heard again. There is carpet visible throughout the Tomahawk which would make such a glass breaking sound impossible.
When the car is in the back of the semi truck and on fire you can see the cable used to pull it out of the truck in front of the car.
In the cafeteria, at the beginning of the movie, a crew member and camera are visible on the far left side of the screen (Widescreen, director's cut).
Ashley can be seen falling through the ice and a few seconds later Rudy follows, when Rudy starts swimming towards Ashley she is already bashing at the underside of the ice trying to escape. However, it would be impossible for Ashley to reach that position in that time as she does it in 16 seconds and Rudy does it in 20 seconds so unless Ashley is an olympic swimmer that isn't possible.