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: During the arrow attack as Captain Willard grabs Chief Phillips to try and make him stop shooting, the sun can be seen setting over his shoulder. Several other shots in this scene, like the next one, were filmed in the mid afternoon with the sun overhead. (02:22:20)
Continuity mistake: As Chief Phillips is shooting he yells, "You savages, come and get it". After he says this the warrior with the spear who eventually kills him can be seen on the shore running in the opposite direction. In the next shot Lance, who is now at the controls, guns the engine. The boat moves forward, not in a circle, yet two shots later when the warrior throws the spear the boat is further back down the river than it was before not further up the river where it should be. (02:22:20)
Continuity mistake: During the arrow attack Captain Willard orders Lance to take control of the boat as Chief Phillips is shooting. When we first see him at the helm look at Lance's head, he doesn't have the broken arrow in his hair. In the next shot he does. (02:22:25)
Continuity mistake: Just before the warrior throws his spear at Chief Phillips there's a shot of Lance at the helm of the boat and we see the right side of the arrow in his hair pointing straight out and the left side pointing upward. In the previous shot both sides of the arrow were pointing straight out. (02:22:25)
Continuity mistake: Captain Willard tries to stop him from shooting but Chief Phillips yells, "you son of a bitch" as he pushes the captain to the floor. In the next shot the captain is up and holding onto the roof of the boat with his left hand. (02:22:25)
Continuity mistake: One spear is thrown and it goes through Chief Phillips horizontally, but in the close-up shot of Captain Willard a fraction of a second before the impact we see the spear in a vertical position in front of the captain's face. (02:22:30)
Continuity mistake: When Chief Phillips is speared we first see Lance at the helm of the boat and it's going forward. In the next shot after Chief Phillips is speared the boat is going around in circles. (02:22:30)
Continuity mistake: In the scene where the Boat captain gets speared, a poor job was done with the whole thing. First, the spear that the native throws is much bigger than the one that is actually stuck in the captain. Second, the spear that is in the captain would have been too small to throw with any accuracy, let alone that distance. Third, a spear of that size would not have had enough velocity to penetrate the captain all the way through his body. (02:22:31)
Continuity mistake: As Chief Phillips is speared he holds on to the roof of the boat with his left hand. The straw has been rearranged from previous shots and is no longer hanging over the side of the roof as it was in the shot before. (02:22:35)
Continuity mistake: After Chief Phillips is speared he falls to the floorboard of the boat. As he falls Lance is not at the helm of the boat where he just was a second ago and where he will be in the next shot when we see his legs. (02:22:50)
Continuity mistake: No one goes near them but as Chief Phillips tries to kill Captain Willard the pile of arrows on the floor of the boat to the left of Phillips' head are rearranged differently between shots. (02:22:55)
Continuity mistake: As Chief Phillips falls to the floor of the boat Captain Willard's left hand is around his armpit. It is the next shot his left hand is near the head of the spear. (02:22:55)
Continuity mistake: Look closely at the shadows going across Chief Phillip's face just before he tries to kill Captain Willard. First they're going from left to right, then in the next shot when he grabs the captain's head, they're going from right to left. This happens several other times in the scene. (02:23:05)
Continuity mistake: After Chief Phillips falls to the floor of the boat Captain Willard kneels down to try to help him. Look closely at Phillips' left hand, there's blood dripping on his knuckle. In the next shot when he grabs the captain around the throat there is no blood on his left hand. (02:23:05)
Continuity mistake: As Lance prepares Chief Phillips' body for burial at sea they are both surrounded by orange smoke. In the previous shot the PBR was surrounded by purple smoke. (02:23:50)
Continuity mistake: As Lance prepares Chief Phillips' body for burial at sea his left foot is on the side of the boat. In the next shot of Chef talking to Captain Willard, Lance is already in the water. (02:23:55)
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: Chef says to Captain Willard, "I thought you were going in to blow up a bridge or some railroad tracks or something" and he has something strapped around his waist. He never touches it but ten seconds later when we see him again it's strapped across the middle of his chest. (02:24:30)
Continuity mistake: Chef says to Captain Willard, "We'll go up there, but on the boat, okay?" and you can see orange smoke blowing from right to left across the screen towards Lance. In the next shot of Lance in the water with Chief Phillips' body there's no smoke. (02:24:50)
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.