Revealing mistake: After the sniper is shot he falls through the wall. Look at his silencer when he hits the ground - it bends where it attaches to the muzzle. A real metal silencer wouldn't do that. (00:41:25)
Plot hole: The original ending planned was a massive tropical storm/water based chase scene. However, this was decided to be too expensive, and was switched for a cheaper, and some say weaker ending. Nonetheless, in Nicholas Cage's final speech, he says "I keep thinking about that tunnel, and what would have happened if I'd drowned." This makes no sense, given that in the new ending he came nowhere near a tunnel or drowning.
Other mistake: Gary Sinise is in the hotel hallway and sees various characters going into different rooms. The camera goes over the top of the wall and we see him from above as he enters a room. The camera continues to track into the room perpendicular to the hallway. Eventually the camera passes over the back wall of Sinise's room and we begin to see these other characters in their rooms. This is impossible, these rooms are not behind his but on either side.
Other mistake: The "first time" the minister gets shot, you hear about seven(?) shots when Kevin kills Rabat. Later, you can only see (and hear) 4 shots. (00:41:25)
Continuity mistake: When Ned Campbell hits the Magnificent 7 slot for a win it had one the reels a single bar, then triple bar then double bar. They then show Rick Santoro and Kevin coming towards them. When we see a first person perspective shot from Kevin approaching them we see the reels all have double bar on them. (00:49:35)
Continuity mistake: After Nicholas Cage spits blood on Gary Sinise's ribbons, you can see that the ribbons got soaked with blood. But a few minutes later, when Sinise is tracking Cage by using the GPS, his ribbons are clean. The white parts of his ribbons are white as snow. Sinise did try to wipe the blood off his ribbons but he could not have wiped off all of the blood stains because the ribbons are made of cloth.
Continuity mistake: When the girl, the Navy guy and the fat guy are in the elevator going up, Nicholas Cage tells the guy watching the video surveillance camera to see what floor they pressed in the elevator. The video guy responds that he can't see what buttons they pressed because the buttons are too small. But when they show the monitor which shows what the elevator camera sees, you see the back of the elevator, not the front where the buttons are. Same when they show the inside of the elevator, and show the camera, the camera is angled from the front to the back of the elevator making it impossible to see the buttons which are on the front of the elevator by the door.