Other mistake: Komerov gets shot in the arm at the start of film, however, he is able to use his arm perfectly even straight after being shot. (00:34:30)
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. (00:52:40)
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