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: 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: 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.
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: When being shot at by the helicopter in the hotel room, the scaffolding that John and Jack make a run for is not visible from the outside shots (to the left of the building).
Continuity mistake: During the opening chase we have a long shot of the blue van turning left onto the main road next to the river - the next shot is the armoured truck doing the same, but in close up the road layout is completely different, and yet they are right behind the blue van.
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.
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.
Audio problem: In the scene in the banquet hall, where the bad-guy is eating a carrot, he throws it on the floor. Subsequently, while chewing on the little bits he has left in his mouth, there comes a sound which is not a chewing-small-pieces-of-carrot sound, but a biting-a-piece-off-a-carrot sound. That sound was way too loud to have been produced by some little piece he had left in his mouth.
Other mistake: When John and Jack are in the ball room, the chopper circles back and begins shooting through the building at them. It is shooting into the far right window straight forward. John and Jack get up and take off running. As they do, you can see the bullets' line of fire moving with them through the building as the chopper tries to hit them. But it cuts to an outside view and the chopper has not moved or turned yet from that spot, nor are the guns turning. It is visibly still shooting forward at the same spot. The line of fire follows Jack and John some more, but the outside view shows the chopper just then start moving to begin following their movement.