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)
Other mistake: The soldiers show Captain Willard his new orders, which are visible to the audience. Note there is no mention of Captain Willard anywhere on the page. (00:08:50)
Continuity mistake: When the soldiers come to the door with Captain Willard's new orders a green piece of paper (money) appears behind his gun lying on the table under the lamp. It's there in the close-up but not when they first walk in. The other pieces of paper in front and to the left of the gun are also moved. (00:08:20)
Continuity mistake: As Colonel Kurtz sits and reads articles to Captain Willard from Time magazine look very closely at the clasp of his dog tag necklace on the left of his neck. Throughout the shots he keeps both hands on the articles that he's reading yet the clasp on his necklace moves down his neck more than an inch without being touched. (02:50:55)
Continuity mistake: As Lance prepares Chief Phillips' body for burial at sea his left foot is on the side of the boat. In the next shot of Chef talking to Captain Willard, Lance is already in the water. (02:23:55)
Continuity mistake: Before the napalm attack we see a shot of the spotter plane flying over Vin Drin Dop and the place hasn't been attacked yet even though the battle has been going on for a while. There's no smoke and the bridge is still intact. (00:47:25)
Continuity mistake: Captain Willard reads Kurtz' file and narrates, "Late Summer, Autumn 1968" as Clean drums in front of him. At first Clean has both sticks on the helmet than in the next shot the right stick is on the helmet and the left is hitting the boat. (01:17:20)
Continuity mistake: At the dinner table General Corman tells Harrison Ford to, "Play that tape for the captain please" and we see a close-up of his watch and it reads 4:37. It's late for lunch but when Harrison Ford brought the can of Budweiser to the general it was lunchtime as his watch read 12:35. (00:12:35)
Continuity mistake: Dennis Hopper speaks a little too loud to Captain Willard while Colonel Kurtz is reading his poetry and he gets mad and throws a bowl of bananas right at them. In the next shot they both duck but nothing comes flying their way, no bowl and no bananas. (02:56:20)
Continuity mistake: Approaching the sampan Chief Phillips says, "These boats are running supplies in this Delta," and Captain Willard is holding Colonel Kurtz' folder it is left hand. In the next shot he's not holding anything in his left hand and using it to lean on the boat. (01:34:35)
Continuity mistake: As they all sit on the boat and read their letters from home Lance dances around with the purple smoke canister. Look closely as the red Vietnamese banner on the shoreline disappears between shots. (01:51:20)
Continuity mistake: The guy on the second patrol boat that throws the flare onto their roof starts out wearing a dark green beret, but in the next shot, when we see him up close, he's not wearing any hat at all. (01:16:30)
Continuity mistake: During dinner Hubert de Marais starts to rattle off all of the places in the world the French have lost wars. In the next shot the wine glass in front of Captain Willard goes from one quarter full to three quarters full between shots. (02:05:30)
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.