Continuity mistake: In an aerial shot a helicopter pilot says, "I got a vehicle on the bridge " but if you look closely there's no vehicle on the bridge until the next shot. (00:41:40)
Continuity mistake: When the woman tries to feed the rice to Captain Willard he absolutely refuses it and the spoon barely touches his lips before she takes it away. The next time we see his face after he spots the colonel there are two small pieces of rice stuck to the right side of his upper lip as he turns to the right after the woman wipes his face. (02:54:00)
Visible crew/equipment: As he gives the captain some water, Dennis Hopper says, "Why would a nice guy like you want to kill a genius?" Look closely at the ladle and you can see the reflections of two crewmember's heads moving in front of the main stage light, one on the left and one on the right. (02:43:00)
Continuity mistake: As they pull up to the French plantation there are several close-up shots of Chief Phillips where you can see Clean's legs lying on the floor board of the boat behind him. As some dead bodies in movies do, they move (six inches to their right) between shots without being touched. (01:56:40)
Continuity mistake: Leaving Hau Phat Clean tells the guys a story about a, "cat in the Delta" and Lance picks up his new water skies then puts them back down again while still holding on to them. In the next shot he's not touching them anymore. (01:12:30)
Continuity mistake: Lance wants the surfboard out of his gun turret so Captain Willard pulls it straight up with both hands. In the next shot he's got the surfboard under his arm. (00:54:45)
Continuity mistake: When the Medevac helicopter first lands in the Vin Din Dop courtyard there are only soldiers on the left side of it putting the injured man in. In the next shot five soldiers and a Vietnamese woman appear standing on the right of the helicopter who weren't there before. (00:44:05)
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: At the Playboy bunnies camp Captain Willard jumps off the boat with his rifle in his left hand. In the next shot as he turns around it's in his right. (01:23:30)
Continuity mistake: In the first close-up shot of the soldier wounded in the courtyard the medic behind him tries to give him some water as the camera pans away to two Vietnamese civilians for a second. In the next shot the medic is still holding the canteen but the injured soldier now has something hanging out of his mouth, that looks like a piece of string, which wasn't there in the previous shot. (00:43:25)
Continuity mistake: In the rear close-up shot of the Vietnamese machine gun nest the soldier in the dark green shirt is to the right of the soldier in the tan shirt who is firing it. In the next shot the soldier in the dark green shirt is behind and to the left of the soldier in the tan shirt. (00:40:45)
Continuity mistake: The cigarette that Dennis Hopper hands to Captain Willard is lit and in perfect shape, however in close-up the cigarette is bent near the filter. In the next shot it is once again in perfect condition. (02:43:20)
Continuity mistake: Hubert de Marais says, "Oh I'm sorry, Captain," as Roxanne makes him apologize for carrying on their conversation in French. If you look at her hair it goes from being in the sunlight, to not, than back again several times in this scene. (02:04:40)
Continuity mistake: The lights on the Do Lung Bridge keep changing between shots. There are many more burned out light bulbs in the shot of Captain Willard and Lance as they leave the boat then there are when we first see the bridge or when the bridge is in the background as they walk past it. (01:42:15)
Revealing mistake: In a close-up of Captain Willard's face as he reads about Kurtz' "Operation Archangel" the sweat droplets on the band-aid are exactly the same as the droplets on his skin. The droplets were obviously sprayed on his face as Band-aids don't sweat. (01:02:50)
Continuity mistake: The paint on Captain Willard's face changes many times throughout the movie. Two very noticeable examples are right after he kills the colonel, where the paint is almost entirely off his face, and several shots later as he leaves the temple heading back to the boat where his entire face is painted a much darker green then before. (03:09:20 - 03:11:50)
Continuity mistake: In the close-up of Dennis Hopper giving the Captain some water he holds the ladle between his first and second finger. In the next shot he's holding it between his thumb and first three fingers. (02:42:45)
Continuity mistake: As they get close to the French plantation dock we can see inside the building and it's dark. Several shots later as Captain Willard is walking around inside the building it's lit up from the inside. (01:56:00)
Continuity mistake: When he first opens the package from his mom Clean is holding a brown envelope with a cassette tape in it. Three shots later as he reads the letter from his mom and listens to the tape, the package has changed to a white carton. (01:51:05)
Continuity mistake: Before they board the sampan Lance says, "It's clear, Chief," and we see a wide shot of the sampan and PBR. No one goes near it, but for just one shot the dress on the clothesline is rearranged. The two straps it hangs from are pushed together. In all the other shots the straps are wide apart. (01:35:40)
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.