Continuity mistake: A guy from Lazaro's boat throws a smoke canister that catches fire on the roof and Chef tries to put it out with a fire extinguisher. When we first see him trying to put the fire out his shirt is dry then the next time we see him his shirt is full of sweat. (01:16:40)
Continuity mistake: Chef and Miss May mess around in the helicopter as he says, "I can fly like the eagle". They start out facing the back of the helicopter then in the next shot they're facing the opposite direction. (01:31:40)
Continuity mistake: Colonel Kurtz drops Chef's head into Captain Willard's lap. At first the head has no blood on it but in the next shot when the captain realizes what it is Chef's face has blood all over it. (02:47:10)
Continuity mistake: As captain Willard, Lance, and Chef stand on the dock they hear the voice of a Frenchmen shouting at them. If you look closely at Chief Phillips on the bridge of the boat, he doesn't have a rifle in his hands but in the next shot he does. (01:57:20)
Continuity mistake: After he sees the sampan Chief Phillips says, "A junk boat Captain. We're gonna take a routine check," and Clean goes from aiming the 60 caliber machine gun behind him to not even holding it at all between shots. (01:34:30)
Continuity mistake: Captain Willard's is not carrying a holster when he approaches the bridge and talks to Chief Phillips about him not pulling over the Vietnamese sampan or when he's tying his shoes as he sits on the front of the PBR. He never leaves the front of the boat to get his gun but as Clean starts machine-gunning the sampan he's wearing his holster. (01:36:15)
Continuity mistake: The camera pans left as Colonel Kilgore has a beach party for the men at the end of the day. If you look closely at Lance he has two cans of the beer to the left of him, a Schlitz and a Budweiser. In the next shot the cans are reversed. (00:31:40)
Continuity mistake: Captain Willard and his two escorts get out of a helicopter and walk up to the guard post on the way to see General Corman. The soldier in the front is carrying some yellow papers in his right hand. In the next shot as they pass the guard the papers are in his left hand. (00:09:40)
Continuity mistake: As he spots the sampan Chief Phillips says, " Clean get on that 60" and the machine gun on the back of the PBR is aiming left towards the shore. In the next shot "Canned Heat" is pointing directly behind the boat. (01:34:25)
Continuity mistake: When we first see Captain Willard in the movie he's looking at the ceiling fan spinning above his head. There's only one fan above his head yet we see two different fans in the scene. The first ceiling fan has a different motor and the acoustic tiles show signs of water damage not seen on the second fan. (00:01:50)
Continuity mistake: In the beginning of the movie as Captain Willard dances around his room there's a red and white can sitting on the left of his mirror. It's there for two shots but then in the next shot when he busts the mirror it's not there and we see a box instead. (00:06:45)
Continuity mistake: During the beach party Captain Willard shows a map to Colonel Kilgore who says, "it's hairy, got some pretty heavy ordinance". We can see behind the captain and the closest person is about fifteen feet away but in the next shot a soldier drinking a beer is behind the captain and Chief Phillips appears walking up behind the colonel. (00:32:35)
Continuity mistake: When Clean first walks up to the sergeant about fuel for the boat there are two posters in the window behind him. The first time we see them their lit up but the second time six seconds later they're not and the blinds behind them haven't been touched. The only thing that's been changed is the stage lighting. (01:04:45)
Continuity mistake: Before the Medevac helicopter explodes in the Vin Din Dop courtyard its main rotor is rotating at full speed. In the next shot as it explodes the main rotor is barely turning. (00:44:10)
Continuity mistake: Just before Colonel Kilgore gets into his helicopter, he says to the trumpet player, "All right, Son, let her rip!" His left hand moves from being in front of his belt to being at his side between shots. (00:34:45)
Continuity mistake: Chief Phillips yells, "You son of a bitch" as he shoots wildly. After he says this and Lance guns the engines look closely at the back of the boat because Chef is not at his machine gun. In the next shot he reappears where he should be firing the rear machine gun "Canned Heat". (02:22:20)
Continuity mistake: As Captain Willard stands in front of Lieutenant Colby his hair is soaking wet with sweat dripping off of it. Several seconds later as they look at the severed heads on the steps his hair is dry. (02:33:10)
Continuity mistake: One spear is thrown and it goes through Chief Phillips horizontally, but in the close-up shot of Captain Willard a fraction of a second before the impact we see the spear in a vertical position in front of the captain's face. (02:22:30)
Continuity mistake: Lance's Playboy bunny gets up and runs around after she's startled by Clean when he taps on the window. She accidentally knocks over a casket with a body in it. The first time we see the body there's nothing behind it in the casket but some dried blood. When we see it again four shots later the blood is gone and the body has some bandages or tape lying behind it's left arm. (01:30:30)
Continuity mistake: When Clean sits down in the back of the boat and opens up the tape from his mom, notice the order of the bullets in the machine gun to the right of the screen. When we first see them they're all packed in order, three shots later as he reads the letter they're uneven though no one has touched them. (01:51:00)
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.