Continuity mistake: Captain Willard introduces himself to Colonel Kilgore and says, "I carry priority papers from Com-Sec intelligence, II Corps". There are three guys in Kilgore's helicopter watching the filming by the side door. This is a wide shot and no other soldier is there but three seconds later another soldier appears standing by the pilot's window. (00:27:25)
Continuity mistake: In the first few scenes with the air cavalry commander, his black hat has a lieutenant colonel rank and a small crossed-sword emblem on it. Later, as his helicopter lands on the beach, his hat has no rank and is emblazoned with a very large crossed-sword Cav emblem. (00:27:26)
Continuity mistake: Captain Willard picks up one of the death cards that Lt. Col. Kilgore threw on a dead body and it's the seven of hearts. This is not one of the cards that Kilgore threw down though. As he was naming each one as he threw it and Captain Willard was walking close behind him. (00:28:05)
Continuity mistake: Martin Sheen's fingers are shown many times in close-ups of him reading files such as after the "Satisfaction" surfing scene. They all look the same except for when he picks up Kilgore's death card. The thumbs on this person's hands are much longer than we see throughout the movie and are not Martin Sheen's. (00:28:10 - 01:13:55)
Continuity mistake: After the death card scene, Captain Willard walks past a cistern and a grenade explodes in it. In this shot you can see that it's sunset but in the next three shots it goes from the afternoon to evening then back to the afternoon again. (00:28:20)
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 Colonel Kilgore leans down to give the VC soldier a drink from the canteen watch closely as the roses on the rosebush to the left of the injured soldier disappear and then reappear between shots. (00:29:25)
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: Colonel Kilgore offers the wounded VC soldier a drink of water and his right elbow is leaning on his leg. In the next shot only his forearm is leaning on his leg. (00:29:45)
Continuity mistake: As Kilgore introduces Lance to his surfing buddies he says to him, " none of us are anywhere near your class though". Captain Willard's cigarette and it's ash gets shorter between shots. (00:30:25)
Continuity mistake: After Lance, Kilgore and his surfing buddies walk away we see three guys playing football and the one without a shirt has his hands up in the air waiting for a pass. In the next shot there are only two men and the shirtless guy is now throwing the football. (00:30:40)
Continuity mistake: After Lieutenant Col. Kilgore introduces Lance to his surfing buddies they all walk away and Captain Willard takes a drag from his cigarette holding it with his right hand. A band-aid appears on his right thumb between shots for the first time in this scene. (00:30:45)
Continuity mistake: In the shot of a priest saying the Lord's Prayer, we see smoke rising from an attack by a flamethrower behind him. In the next shot there's no smoke until the flamethrower fires again. (00:30:55)
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: During the beach party as Captain Willard is saying, "He was one of those guys that had that weird light around him." Note he is holding a cigarette and drinking a Schlitz, with four cans of Budweiser in front of him. In his next shot, just seconds later, there is another can of beer and the cigarette is gone despite the fact he has not moved at all. (00:32:00)
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: Discussing the map with Captain Willard Colonel Kilgore says, "Mike, you know anything about this point at Vin Drin Dop? " and Mike goes from looking at Lance on his right to looking at the soldier on his left between shots during the beach party. (00:32:50)
Continuity mistake: While discussing surfing at the beach party Colonel Kilgore says, "We'll pick your boat up and put it down like a baby where you want it." The cigarette he's smoking here gets longer between shots. (00:33:35)
Continuity mistake: At the beach party LColonel Kilgore stands up and says, "This is the first of the ninth, Air-Cav, son". If you look closely when he stands up the map that they were just looking at is gone. The colonel was holding it, but he doesn't have it nor does Captain Willard. (00:33:40)
Continuity mistake: While he's standing Col. Kilgore says, "I can take that point and hold it is long as I like". Chief Phillips' left hand goes from leaning on his leg to rubbing his face between shots at the beach party. (00:33:40)
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.