Continuity mistake: Just after John says "Jack! I'm not done talking to ya!" It shows the blue van backing up and turning around. The first shot shows its headlights turned on, but the next shot they are off. It happens again later when the van is spun and pinned to the front of the armoured truck. (00:22:20 - 00:27:20)
Continuity mistake: The taxi driver looks back at John and says he doesn't have to pay because he let him sing. The shot from in front shows the steering wheel is clear. But the shot changes to behind John and suddenly the driver's arm is on top of the steering wheel and across it. (00:12:00)
Continuity mistake: When we first see John in the shooting range, the other cop brings him news of Jack. John asks if he is in the hospital or morgue. The other guy says "worse". The shot from behind John shows he is looking right at the other guy. But then the shot changes to the other perspective and suddenly John is looking down a little and in a different direction. (00:05:45)
Continuity mistake: In the taxi, the driver says the line "I sing all the time". As he is saying this, there is a shot change. The shot from in front shows his right hand is barely visible next to the steering wheel and semi low. But the shot from behind shows his hand higher with thumb sticking up above the steering wheel. (00:11:40)
Continuity mistake: As Lucy tells John that it's not his fault, the angle showing her shows John with his mouth open. It cuts to another angle and close up of John and suddenly his mouth is closed. (00:07:10)
Continuity mistake: When the bad guy is eating the carrot in the big room, the amount of carrot eaten changes between shots. (00:46:20)
Chosen answer: No. Bruce Willis (and thus, John McClane) is left handed. But guns are mostly designed for right handed people, so when he isn't holding a gun modified for him, it's easier to use it with his right hand.
Friso94