Continuity mistake: As the boat approaches Kurtz' compound the dead body hanging from the tree on the left of the screen is motionless. Six seconds later as they get a little closer the body is twisting and swaying even though there is no wind and no person goes near it. (02:29:00)
Continuity mistake: As Lance is on the top of the PBR Captain Willard says to himself, "He's close, he was real close" and they shuttle between shots of Lance and close-ups of Chief Phillips at the helm. The straw hanging down from the roof of the boat behind Chief Phillip's head is is hanging down differently in both of these shots. (02:21:05)
Continuity mistake: After the rocket attack Chief Phillips looks back and says, "Chef, Chef check out Clean. Captain, he's hit". Look closely at the blood spatter on that the piece of metal that was behind him during the attack. Later as Lance takes over the helm of the boat there's less blood dripping on it. (01:52:30)
Continuity mistake: There's no indication that Captain Willard didn't leave for his mission immediately after having dinner with the General, being that his R&R was over. That nasty cut on his thumb is all healed without any band-aid on it by the time we see him in the next scene on the PBR. There was also a dark scab on his middle finger that was there as he smoked a cigarette in the end of the scene with the general that has also disappeared. (00:20:30)
Continuity mistake: In the scene where the Boat captain gets speared, a poor job was done with the whole thing. First, the spear that the native throws is much bigger than the one that is actually stuck in the captain. Second, the spear that is in the captain would have been too small to throw with any accuracy, let alone that distance. Third, a spear of that size would not have had enough velocity to penetrate the captain all the way through his body. (02:22:31)
Continuity mistake: In a close-up after he burns the picture of his wife with his cigarette, Captain Willard says to himself, "When I was there all I could think of was getting back into the jungle". Look closely at his left cheek and note a red scratch missing from previous shots and not visible in later shots during his drunken dance. (00:05:20)
Continuity mistake: In the close-up of Chief Phillips piloting the boat up to the French plantation dock look closely at the pair of boots hanging evenly by their shoe laces over the 50 BMG that Chef is pointing towards the dock. He hasn't taken his fingers off that machine gun but when Chef gets ready to leave the boat the boot on the right is now higher than the one on the left. (01:56:10)
Continuity mistake: After Lance and Captain Willard return to the boat Chief Phillips says, "which way captain". As the captain sits on the front of the boat look closely at his tee shirt, he has something underneath resembling a large newspaper or package. When he takes his tee shirt off there's nothing under there except his dog tags. (01:47:55)
Continuity mistake: Before they swing the boat around and head to shore to meet up with Lieutenant Kilgore it's the middle of the afternoon with the sun above them. When they reach the shore in the next shot and get off the boat it's sunset. (00:24:30)
Continuity mistake: As Jerry takes a piece of roast beef from the tray we get a close-up of the captain's table setting. Just about everything has been moved from the previous shot but his bread dish and napkin are the most notable as they have both moved to the right of where they were before. (00:12:10)
Continuity mistake: As they walk on the dock at Hau Phat the storage warehouse behind the motorcycles is very well lit up. In the previous shot as they were docking these areas were bathed in a dim blue light. (01:04:30)
Continuity mistake: The entire French plantation dinner scene is beautifully lit. It looks as though it's sunset until Hubert walks over to the window in middle of the scene. As he stands by the window we can see outside and it's not sunset but midafternoon. Then as he walks to his seat he passes back into the yellow stage lighting again which makes it look as if it's sunset. (02:08:50)
Continuity mistake: At the beach party Lieutenant Colonel Kilgore says, "bring me my Yater Spoon the eight-six". Later when Captain Willard steals this surfboard from his helicopter it's not a Yater Spoon, which has a distinctive flat tail and can be seen at www.yater.com. (00:51:25)
Continuity mistake: At dinner, the Frenchmen sitting to the right of Captain Willard says, "Why don't you Americans learn from us, from our mistakes?" When he says this there's a shadow falling on his face but in the next shot his face is lit up again by the sun. (02:10:10)
Continuity mistake: After the little French boy kisses Hubert de Marais he walks away and we watch from behind as Captain Willard's head turns to the right as he looks at him. In the next close-up of the Captain's face he does the exact same thing again. (02:03:05)
Continuity mistake: After Colonel Kilgore looks at Captain Willard and says, "someday this war's gonna end" he gets up to walk away and the soldier to his right straps his rifle around his right shoulder twice between shots. (00:49:55)
Continuity mistake: Note the boat position as Chef starts to mouth the words to "Satisfaction", by tree line they are close to shore. After less than a two second pause in action, we see that the boat is no longer near the shore or any trees. (01:14:55)
Continuity mistake: When Captain Willard looks out his window at the streets of Saigon you can tell by the shadows that the sun is overhead. But in the next shot the sun is coming directly through the window and shining on his face. (00:04:20)
Continuity mistake: As the helicopters approached Vin Din Dop Colonel Kilgore said to Lance, "We'll come in low, out of the rising sun," but when the helicopters fly over the beach their shadows are directly below them. (00:39:40)
Continuity mistake: After the woman tries to feed Captain Willard some rice he looks to his left and sees Colonel Kurtz standing there with one thin ray of sunlight coming down on his head. We saw this spot in the wide shot when the three soldiers placed the captain near the window and it's in the shade, plus the sun is not coming into the room from above but sideways from the right. (02:54:10)
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.