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: When Jack McClane gets his dad from the burning room at the end, he enters wearing a flak jacket and leaves without it, without enough time to take it off, they then leap into the pool.
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.
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.