That spaceship. All of them actually. Imagine a neon display that can fly.
The entire communication scene with the mothership.
Particularly when the mothership first completes the 5-note phrase, which is so powerful it blows out one of the observation tower's windows.
When the smaller ships repeat the 5-note phrase during their appearance at Devil's Tower; the wave of "they actually responded! We're communicating!" is palpable.
The air traffic control scene where Flight Air East 31 and TWA 517 share a UFO fly-by. An expertly staged scene of just the air traffic controller and his co-workers tensely sitting at a radar wondering what the hell is going on. Finally, when the airplanes comes out safely:
Supervisor: Ask them if they want to report officially. Controller: TWA 517, do you want to report a UFO? Over. (long pause) TWA 517, do you want to report a UFO? Over. TWA Pilot: Negative. We... don't want to report. Controller: Air East 31, do you wish to report a UFO? Over. Air East Pilot (shaken): Negative. We don't want to report one of those either. Controller: Air East 31, do you wish to file a report of any kind to us? Air East Pilot: I wouldn't know what kind of report to file, Center. Controller: Uh, Air East 31, me neither. I'll try to track traffic and destination, over.
A quiet one, but no less awesome for it, and it's a major turning point for Roy. When he and Jillian are captured by the Army, Lacombe and Loughlin interrogate him. Roy gets more and more agitated and nervous, constantly asking, "Who are you people?" Then Lacombe makes a mistake, asking Roy if he's had "a close encounter with something very unusual." It tips Roy off as to what's really going on. He asks, "Who are you people?" once again, but his tone is much calmer, and he has a little grin on his face. He's figured most of it out, and he knows that, whatever his issues are, he isn't crazy. It's real.