Continuity mistake: Captain Willard shreds all of his notes on Colonel Kurtz and narrates to himself, "but the thing I felt the most, much stronger than fear, was the desire to confront him". In a wide shot of the boat we can see that the flag that covered Clean's body is back on top of the PBR. (02:26:20 - 02:27:50)
Continuity mistake: As they approach Kurtz' compound Captain Willard says, "Lance, keep your hands away from the guns" before he climbs to the top of the PBR. Look closely at his T-shirt, which is wet with sweat around the collar, then dry in the next shot. (02:27:30)
Continuity mistake: As they approach Kurtz' compound Captain Willard climbs up to the top of the boat. As he's climbing there's no helmet hanging off the light pole in front but in the next shot as he reaches the top a helmet appears. (02:27:40)
Continuity mistake: As the boat approaches Kurtz' compound the natives in the canoes are looking forward. In the next shot they're facing sideways looking at the PBR. (02:28:15)
Continuity mistake: Approaching Kurtz' compound they pass the natives in their canoes and we see the back of the PBR. Look closely and you can see that the boat's name is painted over. In other shots of the PBR we don't see this mark. (02:28:25)
Continuity mistake: As the boat approaches Kurtz' compound the dead body hanging from the tree on the left of the screen is motionless. Six seconds later as they get a little closer the body is twisting and swaying even though there is no wind and no person goes near it. (02:29:00)
Continuity mistake: Dennis Hopper says, "Zap 'em with your siren, man. Zap 'em with your siren," as they get close to shore. At first there's no smoke and unarmed natives behind him and the smoke changes to red in the close-up. Then in the next close up there's orange smoke and armed troops behind him. (02:29:15)
Continuity mistake: As they approach Kurtz' compound the dead body hanging from the tree changes between shots. At first it's facing outward, then as Dennis Hopper climbs on board it's facing the opposite direction and it's an entirely different body wearing a different jacket. (02:29:30)
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: When Captain Willard climbs onto the top of the boat and again when he shakes Dennis Hopper's hand we see no rips or tears on his green T-shirt. But when he says to Dennis Hopper, "Take who away?" there's a huge rip in his T-shirt under his right arm. (02:29:40)
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: Dennis Hopper walks to the back of the boat and says, "I'll tell you one thing. This boat is a mess man, whoo!" As he stands in the middle of the boat note the machine guns are missing, yet in the following shot they reappear with their ammo. Later, as he moves back to the front of the boat the disappear yet again. (02:30:10)
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: After Dennis Hopper comes onto the boat Captain Willard asks him, "Who are all these people?" The Captain has more dark makeup on his cheeks now than he had when they approached the camp a few seconds ago. (02:30:15)
Continuity mistake: After they first meet Captain Willard looks at Dennis Hopper and says, "Take who away?". The red wind spinner to left of the Captain is in tatters, but a few seconds later when Dennis Hopper walks back to the front of the boat it's back together again. (02:30:20)
Continuity mistake: Dennis Hopper Says, " these are all his children, man, as far as you can see" and we see a large leaf covering Chef's head and held on with a rubber band. Then when Dennis Hopper says," the man's enlarged my mindÂ…. do you know that if is the middle word in life?" there's a different leaf on his head that has much more green in it. (02:30:30)
Continuity mistake: As Dennis Hopper leads Captain Willard up the steps we see the wall with "Apocalypse Now" written in white. In the previous shot there were a lot of sand bags there, now there is just a big boulder. (02:31:35)
Continuity mistake: As Captain Willard approaches Lieutenant Colby there is a woman standing in the crowd to the right of him. The next time we see him a few seconds later everyone in the shot is standing in the same spot except the woman is gone and a man wearing a green beret appears in her place. (02:32:40)
Continuity mistake: As Captain Willard stands in front of him the shrunken head hanging off Lieutenant Colby's rifle is not this same one we saw several seconds ago when the captain first set eyes on him. The second one has thicker darker hair and is attached to the rifle differently. (02:33:00)
Continuity mistake: As Captain Willard stands in front of Lieutenant Colby his hair is soaking wet with sweat dripping off of it. Several seconds later as they look at the severed heads on the steps his hair is dry. (02:33:10)
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.