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.