Continuity mistake: In the car chase scene, Mason is driving the stolen Hummer and he hits a meter maid truck sending it flying into a telephone pole and blowing it up. They slow down the film a little here and show us this hit from several different angles including from above. When they slow down the film you can see that the Hummer is turned sideways in the impact but in the next frame it drives off as if it had just tapped the meter truck and not slammed into it as shown.
Continuity mistake: In the chase scene, Cage is in a real Ferrari F-355 at some points, but the car switches to a replica 'kit car' in various scenes. When it is crushed, you can see the fibreglass kit car body pop off to reveal the Pontiac Fiero guts. I heard our friends from Maranello were not impressed.
Continuity mistake: During the chase scene, just before the Ferrari is destroyed by the trolley, you see Cage dive out of the car and a rear view of the trolley hitting the car. In this shot, you see the complete rear end of the Ferrari, with a blue pickup next to it. In the very next shot, the Ferrari is getting sandwiched between the trolley and the pickup.
Factual error: When Cage gets into the Ferrari, the camera changes for a few seconds showing the gearbox. In slow motion it is obvious that Cage shifts into 3rd gear instead of 1st, however the car makes a very impressive tyre-burning start. The F355 is indeed a very powerful car, but this would be simply impossible to do in 3rd gear.
Continuity mistake: When Nicolas Cage drives through the window in the yellow Ferrari and the shot changes, he is coming out from a different window than in the first shot. In the first shot he emerges from the window to the left of the 7th Street Garage storefront ('Classic Autos' written on the window), but next shot he emerges from the window to the storefront's right. Also, note the now glassless window to the storefront's left, due to a previous take.
Visible crew/equipment: Right near the very end where you have the overhead shot of the bombs hitting the back of the island you see Stanley Goodspeed being thrown through the air by the force of the explosion, and into the water. As he is flying through the air you can see the wires he is attached to, to make him fly.