Continuity mistake: After the napalm attack we see the back of the PBR as the men prepare to continue up the river. Later we see the back again after the scene at the Do Lung Bridge and the boys have a different boat, which now has three lights on its back section. (00:49:00 - 01:49:10)
Continuity mistake: After shooting up the sampan Clean closes his machine gun twice between shots. (01:37:15)
Continuity mistake: A soldier walks up to Colonel Kilgore, as he offers the wounded VC soldier water, and says, "I think one of those soldiers is Lance Johnson the surfer". His floppy hat has the name Latigo printed in the dark letters on the back of it. The next time we see the back of his hat when everyone talks with Lance the name Latigo isn't there even though he doesn't touch it. (00:29:45)
Continuity mistake: After Captain Willard grabs him the sergeant says, "Would you guys like some seats". If you look at the sergeant's desk one of the two flashlights has fallen and the pencils in the pencil holder are rearranged without anyone going near them. (01:05:45)
Continuity mistake: A vehicle on the Vin Din Dop bridge is shot by a rocket from Kilgore's helicopter and Lance says' "nice shot Bill" after he sees the car blow up. Colonel Kilgore's helicopter has surfboards on its sides not rocket launchers as was seen when they took off in the last scene. (00:41:45)
Continuity mistake: Chief Phillips says, "Lance, take a 16 on the bow," and we see him walk to the front of the boat past the spot where Captain Willard was hiding for cover during the attack that killed Clean. The molding was blown off by machine gun fire during the attack, but now it's good as new. (01:55:30)
Continuity mistake: No one goes near them but as Chief Phillips tries to kill Captain Willard the pile of arrows on the floor of the boat to the left of Phillips' head are rearranged differently between shots. (02:22:55)
Continuity mistake: During the arrow attack as Chef is firing the rear machine madly Captain Willard walks from the front to the rear of the boat to try to stop him. Just as he swings into the back part of the boat he slips and falls backwards. In the next shot he's up and running toward Chef. (02:21:50)
Continuity mistake: When Colonel Kilgore shows Lance the surf as they fly over the beach he says, "look, good six-foot swells" and his surf board is not on the side of his helicopter as it is in the next shot when they land. (00:45:10)
Continuity mistake: Just before they leave the USO show the helicopter pilot on the left goes from looking at the controls to looking at the camera between shots. (01:10:10)
Continuity mistake: When Captain Willard shoots the injured Vietnamese woman on the sampan, the T-shirts that we saw before draped over the metal bar in front of Chief Phillips are no longer there even though no one goes near the spot. (01:38:30)
Continuity mistake: When the Captain asks the Chief for the binoculars the boat is standing still but in the next shot as the Captain is watching Kilgore's men they're moving rapidly towards the shore. However, in the next shot, a close-up of the Captain, the ship is back in the same place and standing still. (00:24:40)
Continuity mistake: As they listen to the Frenchmen on the plantation dock, Chef picks up his rifle from the side of the boat. Note this spot and the bloody footprints there, which appear and disappear between shots. (01:57:40)
Continuity mistake: Colonel Kilgore walks over to a VC soldier with a stomach wound and one of his soldiers follows behind carrying a thermos with an orange cap in his right hand and nothing in his left. Kilgore turns and says to this soldier, "Give me that canteen" and in the next shot the canteen appears in his left hand. (00:29:20)
Continuity mistake: When Dennis Hopper says, "The heads, you're looking at the heads, sometimes he goes too far, he's the first one to admit it" look at the two cameras around his neck. At first the lenses are both pointing outward then in the next shot he turns around and the left camera lens is pointing at the ground. (02:33:40)
Continuity mistake: As Chief Phillips falls to the floor of the boat Captain Willard's left hand is around his armpit. It is the next shot his left hand is near the head of the spear. (02:22:55)
Continuity mistake: Look closely at the shadows going across Chief Phillip's face just before he tries to kill Captain Willard. First they're going from left to right, then in the next shot when he grabs the captain's head, they're going from right to left. This happens several other times in the scene. (02:23:05)
Continuity mistake: Lance's facial makeup changes between shots. The area around his eyes and nose changes in the three seconds it takes for Dennis Hopper the jump onto the PBR. (02:29:35)
Continuity mistake: After Chief Phillips is speared he falls to the floorboard of the boat. As he falls Lance is not at the helm of the boat where he just was a second ago and where he will be in the next shot when we see his legs. (02:22:50)
Continuity mistake: After she sits down everyone is eating and Roxanne breaks the silence saying something in French while holding her napkin. At first she holds the napkin with the frills up but in the next shot the napkin is reversed with the frills on the bottom. (02:04:25)
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.