Continuity mistake: Hubert has a discussion with the Frenchmen sitting to the right of Roxanne who gets up and leaves. As he gets up his hands are on table but in the next shot they're at his sides. (02:11:05)
Visible crew/equipment: After the man sitting to the right of Roxanne gets up and leaves there's a wide shot of the table with Captain Willard at the right. If you look closely at his hair you'll see the shadows of crew members moving between him and the stage lighting throughout this shot. (02:11:15)
Continuity mistake: Hubert says to Captain Willard, "We took the Vietnamese, work with them, make something" and the guy sitting on the right of Roxanne who got up and left several shots ago is back. (02:12:15)
Deliberate mistake: After Hubert exit's the French Plantation dinner scene the stage lighting on Roxanne and Captain Willard shuts down abruptly before their close-ups. There's no one there to touch a light switch and we can see outside and the natural lighting hasn't changed. (02:13:30)
Continuity mistake: Roxanne prepares a pipe for Captain Willard and says, "It was the morphine he took for the wounds he suffered in his heart." The shadow of her left hand falls on her face as she holds the needle over the flame. In the next shot, however, the lighting has changed and the shadow is now nowhere near her face. (02:16:40)
Continuity mistake: Roxanne continues to prepare the pipe for Captain Willard and says, "he would rage and he would cry, my lost soldier, and I said to him there are two of you". In the shot of them from the foot of the bed Roxanne's head is almost touching the captain's but in the next shot over the side of the bed she's about a foot away. (02:16:55)
Continuity mistake: As Captain Willard takes a smoke from Roxanne's pipe the pillow he's lying on is light green. Later after they're finished as he lies on his back the pillow is now light red. (02:17:20)
Continuity mistake: As Captain Willard takes a smoke, the shadow of the pipe is on Roxanne's face but in the next shot as she looks at him the pipe's shadow has disappeared. (02:17:30)
Audio problem: As they lie there in bed Roxanne says, "you are alive captain" and you can only see the side of her face. Her jaw is not moving and if you look closely at her face, all she's doing is returning the captain's smile, not talking. (02:18:10)
Continuity mistake: As Roxanne unties the curtains around the bed the scarves draped over the light on the left of Captain Willard are not the same ones we just saw in a previous shot as the captain took a smoke from the pipe. The ones before were red and yellow but now the middle one is primarily green. (02:19:05)
Continuity mistake: After they leave the French plantation Chief Phillips maneuvers the boat through some thick fog and says, "I said I can't see a thing captain I'm stopping this boat, I ain't riskin' no more lives". When he says this line he's looking directly at Captain Willard but in the next shot his head is turned as he looks over towards his right. (02:20:15)
Continuity mistake: As they begin to break out of the fog bank Chef says, "watch it over here, chief, got a stump". Here he's helping Chief Phillips steer the boat with a long pole that he places back on the floor of the boat after the uses it. You can see that it's not hanging over the right side of the boat behind Chief Philips but at the beginning of the arrow attack it's back extending out over the side. Then a few shots later as Captain Willard runs to the back of the boat to stop Chef from firing it's gone completely. (02:20:55)
Continuity mistake: As they begin to break out of the fog bank Chief Phillips says, "Lance on the 50s". Lance doesn't move from where he is on the roof of the boat but Chef goes to the machine gun twice between shots and points it in different directions each time. (02:21:00)
Continuity mistake: As Lance is on the top of the PBR Captain Willard says to himself, "He's close, he was real close" and they shuttle between shots of Lance and close-ups of Chief Phillips at the helm. The straw hanging down from the roof of the boat behind Chief Phillip's head is is hanging down differently in both of these shots. (02:21:05)
Continuity mistake: Lance comes down from the roof of the boat and we get a good close-up look at his makeup. Fifteen seconds later as the arrows start flying his facial makeup is entirely different (neck, nose, ears, bandanna). (02:21:15)
Continuity mistake: Captain Willard says, "Whatever was going to happen, it wasn't gonna be the way they called it back in Nha Trang". Note the light pole in the center of the boat, the second blue light from the top is shot out however there hasn't been any battles since the French plantation scene when all four blue lights were intact. (02:21:25)
Continuity mistake: As he says, "so when you ask me why we want to stay here, Captain" Hubert's face and jacket go from being in the light to being in a shadow between shots. (02:21:30)
Continuity mistake: At the beginning of the arrow attack Chief Phillips yells, "Chef, open up, fire". Before he says this we see a wide shot of the shoreline with no vertical poles sticking up. In the next close-up shot of Chief Phillips there's a red spear stuck in the mud on the shore. (02:21:35)
Continuity mistake: As Chef is firing the rear machine gun there are two belts of ammo on the 60 caliber gun behind him, one hanging out of the gun itself and the other one draped over the gun's protective metal side. In the next shot as the captain runs up to him there's only one belt of ammo. (02:21:35)
Continuity mistake: During the arrow attack Chief Phillips yells "Lance, fire" and we see a shot of Chef on his machine gun ducking the arrows. Look closely at the unmanned machine gun to his right. First it's pointing into the air, then in the next shot it's aiming downward. (02:21:40)
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.