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: 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: After Chief Phillips falls to the floor of the boat Captain Willard kneels down to try to help him. Look closely at Phillips' left hand, there's blood dripping on his knuckle. In the next shot when he grabs the captain around the throat there is no blood on his left hand. (02:23:05)
Other mistake: When Chief Phillips tries to kill Captain Willard there's a shot of the captain's back in the bright sunlight. If you look closely at the center of his back below his right shoulder there's a pressure mark similar to what you see on a hot summer day after a person gets up from sitting in a beach chair for a while. On the PBR we see Martin Sheen's character standing for a long time throughout the entire scene, but he was definitely sitting for a while before this particular shot was filmed. The pressure mark is not in the previous shot. (02:23:20)
Continuity mistake: As Lance prepares Chief Phillips' body for burial at sea they are both surrounded by orange smoke. In the previous shot the PBR was surrounded by purple smoke. (02:23:50)
Continuity mistake: As Lance prepares Chief Phillips' body for burial at sea his left foot is on the side of the boat. In the next shot of Chef talking to Captain Willard, Lance is already in the water. (02:23:55)
Visible crew/equipment: After he tells him what his mission is Chef says to Captain Willard, "That's f***ing typical, shit, f***ing Vietnam mission". Look at the shoreline about 30 feet past the boat as a crewmember ignites a purple smoke canister. (02:24:20)
Continuity mistake: Chef says to Captain Willard, "I'm short and we gotta go up there so you can kill one of our own guys?" as Lance pulls Chief Phillips' body off the PBR and into the water. In the next shot he's already several feet away from the boat. (02:24:25)
Continuity mistake: Chef says to Captain Willard, "I thought you were going in to blow up a bridge or some railroad tracks or something" and he has something strapped around his waist. He never touches it but ten seconds later when we see him again it's strapped across the middle of his chest. (02:24:30)
Audio problem: Lance is singing while he's in the water with Chief Phillips' body and his lips do not match his vocalizing. (02:24:35)
Continuity mistake: Chef says to Captain Willard, "We'll go up there, but on the boat, okay?" and you can see orange smoke blowing from right to left across the screen towards Lance. In the next shot of Lance in the water with Chief Phillips' body there's no smoke. (02:24:50)
Continuity mistake: Captain Willard shreds all of his notes on Colonel Kurtz and narrates to himself, "but the thing I felt the most, much stronger than fear, was the desire to confront him". In a wide shot of the boat we can see that the flag that covered Clean's body is back on top of the PBR. (02:26:20 - 02:27:50)
Continuity mistake: As they approach Kurtz' compound Captain Willard says, "Lance, keep your hands away from the guns" before he climbs to the top of the PBR. Look closely at his T-shirt, which is wet with sweat around the collar, then dry in the next shot. (02:27:30)
Continuity mistake: As they approach Kurtz' compound Captain Willard climbs up to the top of the boat. As he's climbing there's no helmet hanging off the light pole in front but in the next shot as he reaches the top a helmet appears. (02:27:40)
Continuity mistake: As the boat approaches Kurtz' compound the natives in the canoes are looking forward. In the next shot they're facing sideways looking at the PBR. (02:28:15)
Continuity mistake: Approaching Kurtz' compound they pass the natives in their canoes and we see the back of the PBR. Look closely and you can see that the boat's name is painted over. In other shots of the PBR we don't see this mark. (02:28:25)
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)
Audio problem: Approaching Kurtz' compound Lance starts drumming on two tin cans and if you listen closely they get the overdub wrong. At first we hear two distinct pitches, which are the actual sounds, picked up by the microphone but the last time he hits it we hear a third higher pitch which was overdubbed. There are only two cans not three and he doesn't change the way he's holding them therefore you can only have a maximum of two audible pitches. (02:29:05)
Continuity mistake: Dennis Hopper says, "Zap 'em with your siren, man. Zap 'em with your siren," as they get close to shore. At first there's no smoke and unarmed natives behind him and the smoke changes to red in the close-up. Then in the next close up there's orange smoke and armed troops behind him. (02:29:15)
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.