Visible crew/equipment: In the shot of Captain Willard and Lance joking about the colonel Lance says, "how am I going to shoot him the next time he comes around?". Look closely between the two actors as an equipment shadow moves from left to right than back again against the trees behind them. (00:54:45)
Other mistake: Soldiers are already crashing the stage as Bill Graham gets the helicopter crew to rev up the engines but the two Green Beret security guards that are watching the girls have quite a delayed reaction and act as if nothings happening at all. (01:09:40)
Continuity mistake: Just before they leave the USO show the helicopter pilot on the left goes from looking at the controls to looking at the camera between shots. (01:10:10)
Continuity mistake: When Captain Willard shoots the injured Vietnamese woman on the sampan, the T-shirts that we saw before draped over the metal bar in front of Chief Phillips are no longer there even though no one goes near the spot. (01:38:30)
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 listen to the Frenchmen on the plantation dock, Chef picks up his rifle from the side of the boat. Note this spot and the bloody footprints there, which appear and disappear between shots. (01:57:40)
Continuity mistake: Colonel Kilgore walks over to a VC soldier with a stomach wound and one of his soldiers follows behind carrying a thermos with an orange cap in his right hand and nothing in his left. Kilgore turns and says to this soldier, "Give me that canteen" and in the next shot the canteen appears in his left hand. (00:29:20)
Continuity mistake: When Dennis Hopper says, "The heads, you're looking at the heads, sometimes he goes too far, he's the first one to admit it" look at the two cameras around his neck. At first the lenses are both pointing outward then in the next shot he turns around and the left camera lens is pointing at the ground. (02:33:40)
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: Lance's facial makeup changes between shots. The area around his eyes and nose changes in the three seconds it takes for Dennis Hopper the jump onto the PBR. (02:29:35)
Continuity mistake: After Chief Phillips is speared he falls to the floorboard of the boat. As he falls Lance is not at the helm of the boat where he just was a second ago and where he will be in the next shot when we see his legs. (02:22:50)
Continuity mistake: After she sits down everyone is eating and Roxanne breaks the silence saying something in French while holding her napkin. At first she holds the napkin with the frills up but in the next shot the napkin is reversed with the frills on the bottom. (02:04:25)
Continuity mistake: As Chef and Clean sit on the back of the PBR reading their mail, we see Lieutenant Kilgore's surfboard wedged between the machine guns. It's there until the shot when we see Clean after he's been killed, where it disappears. (01:51:40)
Continuity mistake: Just after the rocket attack that kills Clean starts there's a close-up of Lance manning the machine gun in the front of the boat. The Vietnamese spray this area with machine gun fire and chip away a lot of the green paint to his left under the radar dome. The next time we see this spot the paint is untouched. (01:52:00)
Continuity mistake: The Vietnamese fishermen hand Chef the two small pieces of paper that they had in their hands. He reads the first one for a while then grabs the second one from the guy in the middle, leaving them with no papers in their hands. The next time we see Chef two shots later he has only one piece of paper in his hands and is now grabbing a new large identification paper that none of the three had before. (01:35:25)
Continuity mistake: After the boat docks at the Medevac Captain Willard gets out and walks around and it's clear from the wide shot that there's only one helicopter there. When he comes back to tell the guys about the arrangement with the bunnies we see a close-up of this helicopter and it has yellow tipped rotors. The helicopter that Chef and Miss May are in later in the scene is different as it has white tipped rotors. (01:31:50)
Continuity mistake: As the boat docks at Hau Phat it's not raining and we see several motorcycles parked at the right of the dock. In the next shot it's raining and the handlebars of the motorcycles have been covered. (01:04:25)
Continuity mistake: Colonel Kurtz sits at the door to the dark room where Captain Willard is being held reading articles to him from Time magazine, and it's obvious that the light is coming from the door in front of him. The door doesn't close nor does the captain stop looking forward, but the lighting changes throughout the scene. In some of the close-up shots his entire face and neck are lit up and in other shots shadows fall across his face and neck. (02:51:15)
Character mistake: When Colonel Kilgore is handing out death cards to the dead VC he says, "eight of spades". If you look closely at the card that he throws as it flies threw the air it's the six of spades. (00:28:00)
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.