Continuity mistake: Chef asks his playmate, Miss May, to put on a black wig as they sit in the helicopter. When he first reaches for the wig it's on top of a Styrofoam head but in the next shot he reaches for it again and it's on a small table to the right of the Styrofoam head. (01:28:50)
Continuity mistake: Dennis Hopper stands on the back of the boat and says to Captain Willard, "Yeah, well, they think you've come to uh - , to take him away". If you look to the left of the screen you'll see a piece of seaweed hanging off the roof of the boat. When Dennis Hopper walks back to the front of boat it's gone. (02:30:15)
Continuity mistake: In the shot of a priest saying the Lord's Prayer, we see smoke rising from an attack by a flamethrower behind him. In the next shot there's no smoke until the flamethrower fires again. (00:30:55)
Continuity mistake: When they first approach Dennis Hopper we see the water on the left side of the boat past where Lance is sitting and there are no flames on it. After Hopper jumps on the boat and goes to shake the captain's hand we see an oil slick burning in the middle of the water. (02:29:40)
Continuity mistake: After Dennis Hopper walks around to the other side of the bamboo cage Captain Willard turns around to look at him. Now both his upper and lower lips are parched but when we saw him in a close-up before when Dennis Hopper said, "he likes you, he really likes you" only the captain's lower lip was parched. (02:43:50)
Continuity mistake: After the music for "The Ride of the Valkyries" is turned on there are several shots of the helicopters flying in formation and no speakers or surf boards can be seen on them. (00:38:10)
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: As Chief Phillips yells, "you savages, come and get it" Captain Willard grabs him with his right hand to try and make him stop shooting. In the next shot he's holding him with both hands. (02:22:20)
Continuity mistake: While he's standing Col. Kilgore says, "I can take that point and hold it is long as I like". Chief Phillips' left hand goes from leaning on his leg to rubbing his face between shots at the beach party. (00:33:40)
Continuity mistake: Captain Willard thinks to himself about how many men he may have killed in the war and we see the PBR up close for the first time. The crew on this boat is not the same as the crew we'll be meeting shortly because at least four of them are white. (00:19:25)
Continuity mistake: In General Corman's residence Captain Willard walks past the dinner table and there's an extra light green plate between his plate and the chair that's not there later when he sits down for dinner. None of them went near the table. (00:10:20 - 00:11:40)
Continuity mistake: As Chef and Clean have a verbal fight after they leave the Medevac Lance is in the front of the boat putting on camouflage while holding a mirror in his right hand. In the next shot he's leaning on his right arm and holding the mirror in his left hand. (01:33:20)
Continuity mistake: The first time we see the severed heads there's a lot of white dry ice-like smoke to the right of Dennis Hopper. The next time we see this spot several seconds later the smoke is just starting to appear. (02:33:20)
Continuity mistake: When we first see the Frenchmen appear on the dock in the plantation scene there are eleven of them. The next time we see them as Captain Willard approaches there are four and a few seconds later another five more appear out of hiding. (01:57:55)
Continuity mistake: As the Captain passes Francis Ford Coppola there's a flame throwing tank burning down a hut behind him. In the next shot after the helicopter takes off the flamethrower is gone and some Vietnamese wagons are there instead. (00:26:10)
Continuity mistake: In a close-up Chief Phillips he says, "sampan off the port bow" and we see a kaki green T-shirt hanging next to him at the right of the screen. A couple of shots later Captain Willard says, "what up chief" and Phillips takes the T-shirt down. In the next wide shot of the boat the T-shirt is back. (01:34:15)
Continuity mistake: At Kurtz's compound Lance sits at the front of the PBR watching them chop down the dead body hanging from the tree. The machine gun behind him rotates 45 degrees counter clockwise between shots. (02:34:30)
Continuity mistake: As the helicopters first attack there's a long shot of the Vin Din Dop beach and we can see the Viet Cong huts and none of them has a flag waving in front of them. In the next shot of the same spot we see two bright red communist flags. (00:39:50)
Continuity mistake: Hubert de Marais says to Captain Willard, "And this is something that you never understood, you American". The gentleman in the tan jacket to his left lowers his cigar towards the ashtray. In the next shot his hand is resting on the table with the cigar between his fingers then he puts it in the ashtray. (02:06:50)
Continuity mistake: Captain Willard introduces himself to Colonel Kilgore and says, "I carry priority papers from Com-Sec intelligence, II Corps". There are three guys in Kilgore's helicopter watching the filming by the side door. This is a wide shot and no other soldier is there but three seconds later another soldier appears standing by the pilot's window. (00:27:25)
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.