Deliberate mistake: In the scene where the bad guy is attached to the missile and fired, in the split second before it hits the helicopter you can see below it a building called SUN BANK, but the letters are backwards. A close look reveals the likely reason - to the right of the reversed building is one which looks just like the building to the LEFT of the Sun Bank building behind the harrier a few seconds earlier. Most likely they couldn't film the chopper from the right side because there was a building there (the one the camera flies through), so they filmed it from the other side (the same side they'd filmed the harrier from), catching the "Sun Bank" behind, then had to flip it to have everything facing the right way. (02:06:55)
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