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: When Chief throws the binoculars to Captain Willard, Clean puts on his flak vest. 7 seconds later, Clean is not wearing the flak vest, then he puts it on again. (00:24:37)
Continuity mistake: As they watch Lieutenant Col. Kilgore's helicopter battle from their boat the captain says "It was the air-cav. 1st of the 9th" and Clean appears in the middle of the boat under the flag between shots. (00:24:40)
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 approach the shore to meet up with Colonel Kilgore, there's another boat with teeth painted on it's front next to them on their right. In the next shot they arrive on shore and the other boat is much further behind them. (00:25:00)
Continuity mistake: Captain Willard gets off the PBR and goes looking for Kilgore. A large piece of driftwood appears floating in the water to the right of the boat between shots. (00:25:15)
Continuity mistake: As they come to shore to meet up with Colonel Kilgore, the Captain is crouching on the front of the PBR. In the next shot as he jumps off the boat he's standing. (00:25:15)
Continuity mistake: As the men walk on the shore looking for Colonel Kilgore there's a field behind them across the bay. There's only a tank there but in the previous shot as they landed there were four helicopters along with the tank. (00:25:30)
Continuity mistake: As the Captain goes looking for Colonel Kilgore, there's a sampan docked on the shore with it's sail unfurled. In the previous shot, as the PBR approached the shore, the sail had been folded up. (00:25:30)
Continuity mistake: When Francis Ford Coppola appears in the movie as a TV director, he asks the captain to, "Just keep on going," and a small boy is playing on a black Agent Orange drum in the background. If you watch the labeling on the drum you can see that it's been moved between shots. (00:25:50)
Continuity mistake: Captain Willard and the men get off the PBR and walk to their right about 30 feet in the direction of the hut that is destroyed by the boat with the teeth painted on it. In the next shot when they run into Francis Ford Copola they're back to where they started as we see the boat directly behind them. (00:25:50)
Continuity mistake: After the Captain passes Francis Ford Copola he walks up to a helicopter unloading some soldiers. There's no one near the captain but in the next shot after the helicopter takes off he bumps into a soldier. (00:26:05)
Continuity mistake: As the Captain passes Francis Ford Coppola there's a flame throwing tank burning down a hut behind him. In the next shot after the helicopter takes off the flamethrower is gone and some Vietnamese wagons are there instead. (00:26:10)
Continuity mistake: Captain Willard walks up to a soldier and asks him, "Where can I find the CO". At first he has his right hand on the soldier's left arm then in the next shot he's not touching him at all. (00:26:20)
Continuity mistake: When we first see colonel Kilgore's helicopter there's thick black smoke behind it. In the next shot the smoke is grey and sparse. (00:26:25)
Continuity mistake: When Kilgore's chopper lands, Captain Willard is holding his rifle with the strap around his left shoulder so that the butt comes up above his head. In the next shot he's holding it in his left hand and the strap is not around his shoulder anymore. (00:26:40)
Continuity mistake: Clean starts out to the left of Captain Willard, then just before Colonel Kilgore lands he's behind the Captain chasing his helmet. In the next shot as the helicopter lands he's now in front of the Captain. (00:26:45)
Continuity mistake: As Kilgore's chopper lands it blows orange smoke over the men when we see their backs. In the next shot looking in the direction of the helicopter the smoke is nowhere near them. (00:26:45)
Continuity mistake: As Captain Willard walks up to Lt. Col. Kilgore's helicopter there's rain on the windshield. In the previous shot we see the windshield as the helicopter lands and it's dry. (00:26:50)
Continuity mistake: Colonel Kilgore walks away from his helicopter saying, "Body cards, bring my body cards." Behind him is a radioman and an antenna that is kinked at a 45 degree angle. Two shots later the antenna is standing straight up without adjustment. (00:27:10)
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.