Continuity mistake: Colonel Kilgore talks about getting the boat up the river during the beach party and says, "Hell, a six foot peak," and a cigarette appears in his mouth between shots. (00:33:50)
Continuity mistake: Before leaving the beach party Kilgore says, " Lance, go with Mike and let him pick out a board for you." Lance goes from looking down at the ground to looking up at the Colonel between shots. (00:33:55)
Continuity mistake: As they get ready to leave the beach party Kilgore says, "bring me my Yater Spoon, the eight-six". The soldier to the right of Mike has a cigarette in his mouth that is gone in the next shot. (00:34:00)
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: As Colonel Kilgore gets into his helicopter the trumpet player is standing right there next to it blowing charge. In the next shot as the helicopter takes off he's not there. (00:34:50)
Continuity mistake: As he blows "charge" the trumpet player's scarf turns into a collar the last time we see him as the helicopter leaves. (00:35:10)
Continuity mistake: As they approach Vin Din Dop in Lieutenant Colonel Kilgore's helicopter there's a close-up of Captain Willard looking out of the helicopter. If you look closely there's no wind because the helicopter is not flying. In the next shot as Colonel Kilgore talks to Lance about surfing, it is and there's plenty of wind. (00:36:15)
Continuity mistake: As they approach Vin Din Dop, Chef asks one of the other soldiers, "How come all you guys sit on your helmets?", then puts his left hand on his rifle site. In the next shot his hand is four inches below the site. (00:37:05)
Continuity mistake: After the music for "The Ride of the Valkyries" is turned on there are several shots of the helicopters flying in formation and no speakers or surf boards can be seen on them. (00:38:10)
Continuity mistake: In some shots of the helicopters as they approach Vin Din Dop they're above the clouds, but in successive shots they're at or near ground level. (00:38:35)
Continuity mistake: As the VC first hear the helicopters coming an old woman in a pink top with a baby runs across the schoolyard. In the next shot she disappears and most of the school children have changed positions. (00:39:05)
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: As they approached Vin Din Dop over the beach we see the bridge on the left and no sampans with red sails are there. Fifteen seconds later when they come around the other side of the bridge there are three sampans with red sails unfurled. (00:39:40)
Continuity mistake: As the helicopters first attack there's a long shot of the Vin Din Dop beach and we can see the Viet Cong huts and none of them has a flag waving in front of them. In the next shot of the same spot we see two bright red communist flags. (00:39:50)
Continuity mistake: When the helicopters first attack Vin Din Dop we see eight in formation attacking from the beach with the bridge on the left. One second later we're in a helicopter attacking from the other side of the bridge and we can see the entire beach. From this angle we should be able to see all eight helicopters, but we don't and we also don't see any smoke on the beach from the explosions in the previous shot. (00:39:55)
Continuity mistake: In one shot we see the helicopters firing on the huts along the Vin Din Dop beach and the four missiles go directly into the beach nowhere near the huts. In the next shot the middle hut blows up. (00:40:00)
Continuity mistake: In a close-up of a soldier on a helicopter gunship shooting down at the people of Vin Din Dop below we can see the bridge in the background and it's already been blown up. This doesn't actually happen till later in the scene. (00:40:05)
Continuity mistake: The three adjoining huts on the beach with the communist flags in front of them explode twice at different times in the scene. Then they appear again undamaged in another overhead shot of the beach as a helicopter pilot says, "We're taking fire from the holes". (00:40:10)
Continuity mistake: One minute into the attack on Vin Din Dop one of the helicopters flies over the schoolyard. This aerial shot is taken around mid-day as there are no shadows visible in schoolyard, unlike the first shot of the schoolyard at the beginning of this scene, which was done when the shadows were long. (00:40:20)
Continuity mistake: In the rear close-up shot of the Vietnamese machine gun nest the soldier in the dark green shirt is to the right of the soldier in the tan shirt who is firing it. In the next shot the soldier in the dark green shirt is behind and to the left of the soldier in the tan shirt. (00:40:45)
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.