Continuity mistake: As they approach the French plantation we see a close-up of the right side of the boat which was just in a horrific Vietnamese rocket and machine gun attack. There's none of the damage that you would expect to see on the side of the boat. But specifically we saw close ups of where the hand-held machine guns are stored, and the spot where Captain Willard is standing which were all hit with heavy fire and riddled with holes. (01:55:40)
Continuity mistake: As the soldiers crash the stage, Playmate Carrie Foster signs one of her pictures on a soldier's back as he leans over. In the next shot she signs it again. (01:09:40)
Continuity mistake: As Satisfaction plays in the background, Lance is holding on to a white tow cord as he skis. Earlier as they pull out of Hau Phat we see him holding a blue tow cord before he unwraps his new water skis. Thirty seconds later in another shot he is holding the blue tow cord. (01:15:05)
Continuity mistake: As Captain Willard jumps off the boat at the French plantation we see a wide shot of the debris on the dock. The fuel drums to the right of the screen are rearranged two shots later as he walks up to the door. (01:56:25)
Continuity mistake: As the helicopters land in Vin Drin Dop "The Ride of the Valkyries" is still playing but none of the helicopters have speakers hanging out of their side doors to play the music the way they did before. (00:42:30)
Continuity mistake: As they get ready to leave the beach party Kilgore says, "bring me my Yater Spoon, the eight-six". The soldier to the right of Mike has a cigarette in his mouth that is gone in the next shot. (00:34:00)
Continuity mistake: As the boat leaves the USO show at Hau Phat Captain Willard says, "The war was being run by a bunch of four star clowns who were gonna end up giving the whole circus away". He says this as he walks to the back of the boat moving the 60 caliber machine gun on his way so that is faces frontward. In the next shot it's been moved and is now facing sideways. (01:11:40)
Continuity mistake: As he speaks to Captain Willard in the general's residence, Harrison Ford lights up a cigarette, leaving a big puff of smoke in the air behind him as he walks away. In the next shot the air is clear without a trace of smoke. (00:10:40)
Continuity mistake: As he gives the captain some water Dennis Hopper says, "Why would a nice guy like you want to kill a genius?" The tip of Dennis Hopper's right ring finger is black with soot. In the next shot the soot is not there. (02:42:50)
Continuity mistake: As they stand and listen to the Frenchmen shouting at them, the floodlight on the front of the boat, along with the machine gun turret that it's attached to, move about 45 degrees to the left between shots without having any one touch them. (01:57:35)
Continuity mistake: As Lance water skis and Clean dances, Chief Phillips lays down to watch with his head leaning against the port side metal roof support. In the following shot he is leaning on his right elbow no longer near the roof support. (01:15:00)
Continuity mistake: As Dennis Hopper circles the bamboo cage saying, "I know something you don't know..." Captain Willard's earlobe has less blood on it than when Hopper began his walk and talk. (02:43:45)
Continuity mistake: As Captain Willard holds Colonel Kurtz' paper titled, "Commitment and Counterinsurgency" in front of the camera it changes color from yellow in the first shot to white in the second. (01:15:40)
Continuity mistake: Watching the USO show, Clean and Chef start out on the right of the stage with a still photographer and press reporters, who are sitting behind a desk. Later in a rear close-up of playmate Carrie Foster we see the entire right side of the stage but there is no press desk. (01:07:25 - 01:09:00)
Continuity mistake: As Captain Willard arrives to kill him, Colonel Kurtz stands in the doorway looking at the tribal festival and it's not raining, but in the next shot of the Captain, with the festival in his background, it is now raining. Finally, in the next shot, as the Captain runs to the doorway, it is again no longer raining. (03:06:10)
Continuity mistake: Before they arrive at the French plantation there's a shot of the back of the boat with Clean's dead body lying there. If you look closely the blood splatter is entirely different from the shot when Chief Phillips turns around and first sees that Clean's been killed. The two main differences are that at this point there's blood on the rear machine gun where there wasn't any before, and there's no blood on the right of the V shaped support bar of the 60-caliber machine gun where it had been covered prior. (01:55:40)
Continuity mistake: As Kilgore introduces Lance to his surfing buddies he says to him, " none of us are anywhere near your class though". Captain Willard's cigarette and it's ash gets shorter between shots. (00:30:25)
Continuity mistake: As Chef and Captain Willard are walking through the jungle looking for mangos Chef says," I was supposed to go to Paris" as he's walking over the roots of a huge tree. He continues talking but in the next shot he's out in the open, nowhere near the roots of that tree. (00:57:00)
Continuity mistake: As they approach Vin Din Dop, Chef asks one of the other soldiers, "How come all you guys sit on your helmets?", then puts his left hand on his rifle site. In the next shot his hand is four inches below the site. (00:37:05)
Continuity mistake: As Kilgore's chopper lands it blows orange smoke over the men when we see their backs. In the next shot looking in the direction of the helicopter the smoke is nowhere near them. (00:26:45)
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.