Continuity mistake: During the "bridge is out" scene, Harry's helicopter is parallel to another chopper to the right of it. The chopper to the right is in front of and then behind Harry's chopper depending on the angle.
Factual error: Like all jet fighters, the Harrier/AV-8A has as light an airframe as possible. It is not built for sturdiness. Having worked on Harriers for many years, I can tell you that the damage this one would sustain after crashing into buildings and being shot at and hammered with debris would see it dropping out of the air like a brick.
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