Continuity mistake: As they approach the severed heads Dennis Hopper says, "Wrong, wrong, if you could've heard the man just two days ago". The lock of hair falling over the left side of his bandanna is combed differently between shots. (02:33:35)
Continuity mistake: After Dennis Hopper comes onto the boat Captain Willard asks him, "Who are all these people?" The Captain has more dark makeup on his cheeks now than he had when they approached the camp a few seconds ago. (02:30:15)
Continuity mistake: As Captain Willard approaches Lieutenant Colby there is a woman standing in the crowd to the right of him. The next time we see him a few seconds later everyone in the shot is standing in the same spot except the woman is gone and a man wearing a green beret appears in her place. (02:32:40)
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: 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 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 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: 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: 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 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: After Captain Willard emerges from the room from killing Colonel Kurtz, he has a great deal of blood and oil on his chest and shoulders. When he grabs Lance to go back to the PBR he has mud and water droplets on his chest. (03:13:20)
Continuity mistake: As everyone sits down to have dinner at the General's all the glasses are empty. The next time we see them they're full but no one went around the table filling them. (00:11:40)
Continuity mistake: As Dennis Hopper walks up to the bamboo cage where Captain Willard is being held, a purple haze surrounds them. In the next shot when Dennis hopper gives him a drink of water the purple haze is gone. (02:42:40)
Continuity mistake: As the general reminisces about Colonel Kurtz being a man of, "wit and humor" the roll on his plate moves and changes from being whole to having a bite out of it and back. (00:14:40)
Continuity mistake: After the General says, "And very obviously he has reached his" there's a close-up of Captain Willard and his face is dry. The next time we see him a few seconds later his face especially around his chin is sweaty. (00:17:10)
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: 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: After Chef rips the picture from his Playboy magazine he crouches down. In the next shot as he's taping it up he's standing. (01:12:15)
Continuity mistake: As Chief Phillips is shooting he yells, "You savages, come and get it". After he says this the warrior with the spear who eventually kills him can be seen on the shore running in the opposite direction. In the next shot Lance, who is now at the controls, guns the engine. The boat moves forward, not in a circle, yet two shots later when the warrior throws the spear the boat is further back down the river than it was before not further up the river where it should be. (02:22:20)
Continuity mistake: As Chef is firing the rear machine gun there are two belts of ammo on the 60 caliber gun behind him, one hanging out of the gun itself and the other one draped over the gun's protective metal side. In the next shot as the captain runs up to him there's only one belt of ammo. (02:21:35)
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.