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.
Continuity mistake: When John is in the taxi in Moscow, there is one shot of the taxi with a sticker in a bottom corner which disappears.
Continuity mistake: When arriving in Chernobyl from Moscow it seems to be the same night, although it is over 800km, plus their car is bright and shiny when they arrive despite driving through the rain.
Continuity mistake: When the masseur starts to strangle Viktor, he drops his phone. When the camera angle changes, the phone is 10 feet away from them.
Continuity mistake: When John and Jack steal a car to go to Chernobyl, the trunk had guns in it, but no black vests, which is what they find the second time they open the trunk, at Chernobyl.
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.
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.
Chosen answer: No. Bruce Willis (and thus, John McClane) is left handed. But guns are mostly designed for right handed people, so when he isn't holding a gun modified for him, it's easier to use it with his right hand.
Friso94