Continuity mistake: As Captain Willard smokes his cigarette ,Dennis Hopper says, "I'm curious. I'm very curious. Are you curious?" The captain has the cigarette between his lips pointing upward, but the in the next shot the cigarette is pointing downward and the ash is longer. (02:43:40)
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: 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: Colonel Kurtz drops Chef's head into Captain Willard's lap. At first the head has no blood on it but in the next shot when the captain realizes what it is Chef's face has blood all over it. (02:47:10)
Continuity mistake: When the captain realizes that Chef's head is in his lap he moves around violently trying to get it away from him. We can see that both his legs are tied up with wire but in the next close-up of Chef's head on the ground the captain's foot is freely moving around. (02:47:20)
Continuity mistake: When Captain Willard shakes Chef's head off of his lap it falls into the mud face down and in the dark. In the next shot the head is face up and in the light. (02:47:25)
Continuity mistake: Colonel Kurtz sits reading articles from Time magazine facing the captain and the sun is behind him shining right into the doorway. When we first see Captain Willard locked up in this room he's facing Kurtz and the beams of sunlight are coming in from his left, which is 180 degrees in the opposite direction from the shots of the colonel. (02:48:30)
Continuity mistake: As Colonel Kurtz opens up the steel doors to the room where Captain Willard is being held we see thick black smoke engulfing the entire area behind the colonel. They cut away to the captain for few seconds then back to the colonel as he stands in the doorway, this time with no smoke at all behind him. (02:49:05)
Continuity mistake: As Colonel Kurtz sits and reads articles to Captain Willard from Time magazine look very closely at the clasp of his dog tag necklace on the left of his neck. Throughout the shots he keeps both hands on the articles that he's reading yet the clasp on his necklace moves down his neck more than an inch without being touched. (02:50:55)
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)
Continuity mistake: Colonel Kurtz leaves after he finishes reading the Time articles and there's a close-up of Captain Willard's face and chest. He's soaking wet in the close-up but in the next shot, as he collapses trying to leave the room, his face and chest are dry and there isn't as much dirt on the left side of his chest. (02:52:25)
Continuity mistake: Three soldiers carry Captain Willard into a room by a window where a woman gives him some water from a ladle. As first the sunlight falls across his waist then in the next shot as she gives him the water the sunlight is now on his face and chest. (02:53:35)
Continuity mistake: After the woman gives Captain Willard some water she tries to feed him rice from a spoon, which he doesn't eat. In the previous wide shot of the entire area there is no bowl of rice anywhere, there is only the pitcher of water at her feet and the rice bowl just appears. (02:53:55)
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)
Continuity mistake: After the woman tries to feed Captain Willard some rice he looks to his left and sees Colonel Kurtz standing there with one thin ray of sunlight coming down on his head. We saw this spot in the wide shot when the three soldiers placed the captain near the window and it's in the shade, plus the sun is not coming into the room from above but sideways from the right. (02:54:10)
Continuity mistake: Dennis Hopper speaks a little too loud to Captain Willard while Colonel Kurtz is reading his poetry and he gets mad and throws a bowl of bananas right at them. In the next shot they both duck but nothing comes flying their way, no bowl and no bananas. (02:56:20)
Continuity mistake: As Colonel Kurtz reads his poetry out loud we see Dennis Hopper gesturing with both hands as he speaks with the captain. When the colonel gets mad and throws the bowl of bananas at them Dennis Hopper is holding his camera in his left hand. His bandana is also rolled up differently with the corner sticking up in one shot and down in the other. (02:56:20)
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: Captain Willard enters the temple after he kills a guard and there's a great shot of him holding the machete as it glistens in the light. He just slit someone's throat not two seconds before and there's not an ounce of blood on the blade and it's not even the same machete he was holding three shots ago when we see his silhouette in the festival lights. The first machete we see has a thinner blade with a hook on the end of it and a different handle. (03:07:05)
Continuity mistake: There's a perfect backlit shot of Captain Willard as he swings at Colonel Kurtz and he's now wielding a third machete as he kills him. This one has a square hatchet like blade attached to a long handle. (03:07:45)
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.