Revealing mistake: In the major helicopter scene when Ride of the Valkyries is played, the actual tape isn't going over the playing heads. (00:37:29)
Revealing mistake: A Medevac helicopter lands in the courtyard and later explodes when a Vietnamese woman throws a grenade into it. The copter that lands is not the one that explodes. The front of the helicopter that blows up is older and beat up and the window on the pilot's door does not have any green sun shade on top as the other chopper had when it landed. The one that explodes is also on a platform that collapses as it blows up. (00:44:15)
Revealing mistake: After they ditch Kilgore they dock the PBR on the side of the river. The film jumps here as the camera hits a tree branch as it zooms in on them. (00:53:30)
Revealing mistake: In a close-up of Captain Willard's face as he reads about Kurtz' "Operation Archangel" the sweat droplets on the band-aid are exactly the same as the droplets on his skin. The droplets were obviously sprayed on his face as Band-aids don't sweat. (01:02:50)
Revealing mistake: Dennis Hopper says to Captain Willard, "He said 'If you take my picture again, I'm gonna kill you', and he meant it". Look closely at the dead bodies behind them because they're all moving. (02:32:05)
Revealing mistake: Colonel Kurtz reaches down and catches a fly in his hand and then lets it go. If you look closely the four fingers of his right hand are clinched when he reaches down because the fly is already in his hand. (02:55:00)
Revealing mistake: As Captain Willard takes his second swing at Colonel Kurtz there is a "spark" superimposed against the wall behind his head, which is to depict the contact point of the blade to the wall. However, the blade is actually resting on the Colonel's back, nearly a foot away at that time. (03:07:45)
Revealing mistake: As Captain Willard stands on the steps of the temple there's a wide shot of the natives. If you watch closely you'll see the movie jump. (03:12:30)
Revealing mistake: When Marlon Brando throws Chef's head to Martin Sheen, you can see Chef's head breathing in the close up shots.
Revealing mistake: In the celebration scene in the Buddhist Temple, a boy asks one of the characters for money. This would be fine, except he's speaking in Filipino and the film is set in Vietnam.
Answer: It's not any specific song; it's just the kind of generic piano music you'd hear at dinner at a high-class restaurant of the era. Think of scenes in movies, films, etc. set or made in the '50s and '60s, where the characters go to a nice dinner and there's someone at the piano playing unobtrusive music to accompany the food/conversation.