Continuity mistake: During the scene when Arnold is taking off in the harrier jet, the pilots hide behind a squad car. One pilot is holding his sunglasses. It switches angles and he no longer has sunglasses on. Then his hand moves and they appear as if they had fallen off and he was grabbing them. A few frames later they disappear again. If you look closely, it was obvious they were CGI'd in during editing.
Continuity mistake: In the scene where Harry discovers Helen is having an affair and he's walking across the road. Between the wide and close up shots his wedding ring appears in the close up shots and disappears in the wide shots.
Continuity mistake: When Harry, Helen and Juno are in the private jet, the amount of lipstick smear on his face changes between shots.
Other mistake: When Harry fires the Harrier's Sidewinder missile with the lead terrorist attached to it, he has to switch on the "master arm switch". That switch would have already have been enabled in order to fire the Harrier's gun.
Continuity mistake: When Harry dances the Tango with Juno there's a wide shot of the place, in the immediate close-up two guards appear out of nowhere behind Harry.
Chosen answer: He didn't really. Harry just knew he was heading up. He pressed the top floor to get the elevator moving and kept an eye on him on the way up. If the terrorist's elevator suddenly stops, Harry can press the button for that floor to stop his elevator.
XIII