Continuity mistake: Lance is with his Playboy Bunny spreading makeup on her forehead as she says, "They make you do things that you don't want to do." Later as she says, "I wish I could find, just one person," he puts the make up on her forehead again. (01:30:05 - 01:31:05)
Continuity mistake: Dennis Hopper walks up the steps to the bamboo cage where Captain Willard is being held and gets some water from a fountain about five feet to the right of the cage. In the next shot as he turns around the cage is right there next to him. (02:42:45)
Continuity mistake: As Colonel Kilgore flies over looking for his surfboard the boat is docked with it's bow towards the shore in some shots and it's stern towards the shore in others. (00:54:10)
Continuity mistake: As Chef tries to put the fire out with the fire extinguisher Captain Willard is hanging over the side of the boat with Clean as they try to escape the flames. In the next shot and as chief Phillips walks around him he's behind the helm of the boat near the Playboy picture that Chef taped up. (01:16:50)
Continuity mistake: In the close-up of the General when he says, "He joined the special forces.", note his collar is closed up more and they way the front of his hair is combed changes between shots. (00:14:40)
Continuity mistake: During the arrow attack Chief Phillips yells "Lance, fire" and we see a shot of Chef on his machine gun ducking the arrows. Look closely at the unmanned machine gun to his right. First it's pointing into the air, then in the next shot it's aiming downward. (02:21:40)
Continuity mistake: Just after Captain Willard grabs the sergeant by the throat his cigarette appears back in his mouth between shots, than disappears again in the next shot as he walks away. (01:05:40)
Continuity mistake: Dennis Hopper walks to the back of the boat and says, "I'll tell you one thing. This boat is a mess man, whoo!" As he stands in the middle of the boat note the machine guns are missing, yet in the following shot they reappear with their ammo. Later, as he moves back to the front of the boat the disappear yet again. (02:30:10)
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 Hubert de Marais explains, "The French officer mentality," to Captain Willard, Roxanne goes from looking at the waiter on her left to looking at Hubert on her right between shots. (02:05:15)
Continuity mistake: Captain Willard reads on uninterrupted from "Commitment and Counterinsurgency" by Colonel Kurtz who says in his report, "if they were committed this war can be won with a fourth of our present force". The weather changes from not raining to raining, back to not raining again between shots. (01:15:40)
Continuity mistake: As Colonel Kilgore calls out to the soldiers surfing in the water Captain Willard's band-aid on his right cheek appears out of nowhere for the first time in the movie. He had no band-aid on his face before this and we don't see him put one on, and there's no indication from the last time we saw his face that his scar started to bleed. (00:47:00)
Continuity mistake: Before Captain Willard walks into General Corman's residence the front door is in the shade. In the next shot as he walks through it's lit up with sunlight from behind. (00:10:00)
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: As Dennis Hopper and Chef walk away Lieutenant Colby towards the severed heads when Chef says,"He's gone crazy!" note Hopper's hands move from his sides to raised in one cut. (02:33:30)
Continuity mistake: After the tiger attack Chief Phillips backs the boat out away from the shoreline and says, "Clean bring that 60 forward" well after the boat has cleared the tree that has been camouflaging it. In the next shot the tree is hitting Clean in the face. (00:59:20)
Continuity mistake: Dennis Hopper says to captain Willard, "the man really likes you" as he hands him the cigarette. In the close-up look closely at Hopper's right hand, as a cut appears on his forth knuckle that wasn't there in the previous shot. (02:43:20)
Continuity mistake: As they stop at the Playboy Bunnies' camp, two barefoot soldiers run out to meet them. When they first come out there's a red and white oil drum standing in front of their tent. In the next shot it's overturned but later when they walk back into the tent it's upright again. (01:22:55)
Continuity mistake: As they leave Colonel Kilgore on the beach at Vin Drin Dop the boat sails off to the left of the screen towards the bridge that was destroyed earlier in the attack. If you look at the far left of the screen there's a small Vietnamese temple with no fire anywhere near it. As they pass closer to the temple a large fire is now burning in front of it. (00:51:50)
Continuity mistake: Captain Willard says to Chief Phillips, "how long has that kid been on his boat?" and a long green piece of fabric is dangling off the roof of the boat behind the Chief. In the next shot of the captain, it's gone. (01:19:20)
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.