Continuity mistake: In the taxi scene were you see the ambulance escort pull onto the road; you see John swing around a corner going very fast, when Zeus says "slow the fuck down McClane". He gets ready to pass a large black car but the next shot (an in car shot) you can see that he never passes the car.
Continuity mistake: When they drive through the park and jump off the rock they land on a pile of leaves which covers the hood. Some of those leaves fall off but not all of them - in the next shot the hood is completely clean.
Continuity mistake: There is a scene where Samuel L. Jackson and Bruce Willis are in a crowded park, and they have to defuse a bomb by measuring out water. Before they do that, he picks up a cell phone and calls a bad guy with it. When he is beginning the conversation, the cell phone antenna is down. They change to a different angle, and the antenna is up.
Continuity mistake: When Willis washes the blood off his face after shooting the bad guy in the elevator, the "towel" he wipes his face has no blood on it at all. Even after washing the worst off with the water it would still be full of blood.
Continuity mistake: When the taxi is driving through the park, the damage to it is constantly changing. Most noticeable is a dent on the driver's front wing.
Continuity mistake: When Bruce and Sam are driving through the park and jump the concrete ramp out into the street, they land (or drive over) 2 taxi cabs parked there. In the close-up shot of their taxi crushing the front and rear of the other 2 parked ones, you can see that an entire wheel disconnects from one of the parked taxis and begins to fling out into the street with great speed. In the following wide-angle shot of their taxi swerving into the road, that wheel is nowhere to be seen. It should have bounced across the road.
Continuity mistake: In the subway scene, when carrying it before it starts to mix, the door is hanging off on the left side. When it starts to mix, the door is hanging off on the right side. There could be some time that he could rotate it, but with him using his left hand to tell people to move to the front of the car and grabbing the poles, he wouldn't be able to rotate it.
Continuity mistake: When Samuel L Jackson runs down the stairs in the subway station, he checks the clock, which reads 10:19:10. Then when the train destroys the clock a bit later, the time's now 10:20:24, though well over 2 minutes has passed (only counting Samuel L Jackson's scenes, as Bruce Willis' presumably take place simultaneously. Counting them separately it's even longer). (00:33:00 - 00:36:30)
Continuity mistake: When McClane (Willis) approaches the dump truck in the aqua duct, the driver pulls an Uzi submachine gun onto his lap. The camera then cuts to McClane being seen in the door mirror of the truck, then cuts again to the cab being shot full of holes by McClane. The gun on the driver's lap changes to an MP5K (in this case, a Daisy MP5K Airsoft Replica).
Continuity mistake: The sun is coming up behind McClane at the end. Particularly noticeable in the shot where McClane is shooting at Simon. The previous and following shots show a black sky.
Continuity mistake: The damage to the sedan during the shootout on the road changes. The windshield goes from being normal to full of cracks.
Continuity mistake: When the cab drives between the two trucks it comes out without a scratch. When it crosses the park it is damaged all over.
Continuity mistake: After exiting the aqueduct, McClane falls in a puddle, hair slick, soaking wet and covered in mud. Zeus calls him and McClane turns around. In a brief shot from behind him his hair swaps to clean and fluffy.
Continuity mistake: In the taxi, when Zeus is telling John his name and asks if he has a problem with that, John's hand is not against his head. In the next shot it is.
Continuity mistake: Near the end, after the huge gold heist, Simon Peter Gruber and his psychotic lover, Katya, engage in rough celebratory sex, ripping off each other's clothing, such that Katya's upper torso and black lace brassiere are fully exposed. A few minutes later, when John McClain interrupts their sex, Katya's shirt is fully closed.
Continuity mistake: The cab drives in between two trucks and drives further up. When McClane says "I didn't say Park Drive" watch the rear window and the truck he passed by 50 meters away is now really close behind.
Continuity mistake: Before the cab drives through Central Park McClane slams on the brakes. Skid marks from previous takes can be seen on the pavement.
Chosen answer: He sees the reflection of his friend's badge number that he remembered from their conversation about the lottery earlier, so knows the badge was taken from his dead friend.
Captain Defenestrator