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: When we first see John, he is in the police shooting range. He has on protective head phones which he takes off and sets on the table in front of him as the other cop comes in. He and this cop talk about Jack, and when they finish, they shake hands. The mid range shot of them shaking hands shows the head phones still on the table. It then cuts to a far shot and now the head phones are gone while the two finish the hand shake. Careful which table you are looking at, as the angle makes it confusing. The head phones were on the table with the red thing on its left side. (00:06:50)
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: 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: When John gets out of the taxi, the window is open. When he closes the door, the window is shut. (00:12:00)
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 Jack and Yuri escape from the courthouse, both have their hands cuffed. After getting in the blue van for the first time, they still have the cuffs on each hand, but they are no longer chained together. (00:19:00)
Continuity mistake: In the car chase near the start, the blue and white cars hit bumper to door. When the tank type car hits them they are end to end. (00:22:00)
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 mobile tank rips a door nearly completely off a blue van. When John hits it, there is less damage to the door. (00:22:50)
Continuity mistake: In the car chase, the blue van is hit and the left side headlight dislodges and is dangling down for most of the chase. But in one far shot where the van is taking a turn, it is suddenly switched to the right headlight that's dangling. (00:23:00)
Continuity mistake: When John and Yuri are standing in front of the crane and talking about their children, John's arms go from crossed to by his side, back to crossed a couple times between shots. (00:39:35)
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)
Continuity mistake: Just after John asks Jack if he is "gonna cry a little" before he pulls the bolt out of him, Jack leans his head back. The next shot, Jack's head is down. Throughout this scene, his head keeps changing position between shots. Also noticable right after John says "You shot?" (00:58:25)
Continuity mistake: When John and Jack are discussing if he meant Chernobyl, the blood on Jack's face disappears instantly. (01:00:50)
Continuity mistake: At the end, Jack and John fall into the pond and get soaked. As they walk out of the building their clothes are completely dry. (01:29:15)
Continuity mistake: At the end, the wreckage of the helicopter changes position instantly. Note the position where the rotor blades are. In one shot they are on the side, then on top. (01:29:35)
Continuity mistake: In the scene when Yuri's daughter is getting away from the hotel, the color of the chopper changes from green to brown between shots.
Continuity mistake: Throughout the blue van chase, the damage to the van is constantly changing/repairing itself.
Continuity mistake: During the chase with the blue van, it keeps changing model. Starts with a van with high roof, than low roof, high roof again. And this goes on and on.
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