Continuity mistake: McClane's fireman's jacket gets progressively bloodier throughout the film, but around the time when he is fighting the terrorists on the planes wing, it is miraculously clean again. McClane is not wearing it, but it does get cleaner. (01:45:50)
Continuity mistake: In the airport lobby, when the two policemen come at the bar they have "snow" all over their clothes. In the next shot they are shown from behind sitting at the bar and Lorenzo's brother has no snow on his jacket. Seconds after Mc Clane comes to talk to them and the cop has snow on his shoulders again.
Continuity mistake: When McClane grabs Marvin the janitor and pushes him against the lockers, McClane's thumb changes position on the gun, some shots it's on the hammer, other shots it's around the handle.
Continuity mistake: When John and his wife hug, his hand suddenly appears on her head.
Continuity mistake: When the general exits the plane with Colonel Stuart, nobody shuts the door. It is closed in the very next shot.
Continuity mistake: When Barnes and the SWAT team reach the Annex Skywalk, they get on the moving sidewalk. Before the terrorist stops the moving sidewalk by pressing the button, the sidewalk is already stopped, even though the light was still green at the time.
Answer: Because the police were moments away from arriving at the scene. They needed as much time to get away without being tracked. Every moment counts. And a target rocking about a few hundred feet in the air doesn't seem to be such an "easy target".
XIII