The moment the aliens in the mothership realise they can open a dialogue with the humans. The 5-tone greeting is repeated from the human side a few times, only getting a few discordant toots and trumpets. Then it's played again, and once the third tone is hit... buh BAAAHHHHHM plays from the mothership loud enough to break windows and make the structures rattle. Then the conversation REALLY kicks off.
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 middle one does what almost looks like a happy spin, as though saying "They finally get it!"
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.
Another quiet one. Scientists at the Goldstone radio observatory have been receiving a series of numbers from space but don't know what they mean. During their enthusiastic debates, the translator, a meek and bookish guy who has for the most part stayed in the background nervously asserts himself.
Laughlin: Excuse me. Excuse me... Before I got paid to uh, speak French I, uh... I used to read maps. This first number is a longitude. (The room falls silent, all eyes on him.) Uh, yeah. Two sets of three numbers. Degrees, minutes, and seconds. The first number has three digits and the last two are below sixty. Obviously, it's not in right ascension and declination on the sky. These have to be earth coordinates.
Lacombe argued that out of all the humans on the planet, the people who came to Devil's Tower because of the alien's influence "belonged" there because they were invited. When Neary, Jillian and a third detainee bolt from the Army checkpoint and make a run for the mountain, Lacombe spots them sprinting away. He says nothing, only smiling as they go.
Neary and Jillian drive cross country in a family station wagon to get past the military checkpoints and barricades blocking their way to their unseen destination. They stop the car and the mountain is visible in the reflection of the windshield, when they get out and climb a berm topped with barbed wire. As they ascend, the music swells, and they (and the viewers) get their first look at Devil's Tower.