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.
Factual error: When Yuri's daughter is getting away from the hotel tower, she has to walk to the next building located in front of the tower's window to take the chopper. It should take several minutes, but she does it in a few seconds. (00:48:25)
Plot hole: When Jack and John are on their knees in the hotel, with their hands zip-tied behind, Jack manages to use a hidden knife to cut his bindings and starts kicking bad guy butt. Jack immediately joins the fray but a careful review shows that at no point did John use his knife to free Jack.
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.
Continuity mistake: During the opening chase the chase goes along the river from left to right as you look at the screen. They make a turn and now go from right to left as you look at the screen, along the same river.
Revealing mistake: When the armoured truck hits the first parked car you can see the smoke appear at the side of the car and a jet of smoke when it flips from the air cannon.
Revealing mistake: In the opening chase with the armoured truck it comes up behind a blue car that is already dented on the near side, which is the side it slides round to so the truck hits it. It then gets pushed onto a silver van that is completely wrecked from previous takes.
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)
Plot hole: When John has Yuri pinned to the uranium boxes, Yuri reaches into his coat and turns on his walkie talkie so his daughter and minions can hear. John McClane doesn't notice and he is right there. There are two things wrong with this. We hear the beep the radio makes when it is turned on, and it was loud enough that John and Jack would have easily noticed. But even if they didn't hear it, there is another issue. John is a New York cop, or even a detective. As such, he would have extensive training for dealing with armed men, and he would have noticed Yuri reaching into his coat. Even if he didn't hear the radio beep, he would have stopped Yuri's hand or done something, assuming Yuri was reaching for a gun. (01:18:15)