Other mistake: Captain Willard inquires from two soldiers manning a machine gun, "Who's the commanding officer here?" The two can't kill the enemies "out there by the wire" so they ask their friend "Roach" for some help. As "Roach" walks over he turns off a tape recorder playing some Jimmy Hendrix riffs. If you look closely at the buttons of the tape recorder, it was never on in the first place. (01:45:50)
Other mistake: During the arrow attack Chief Phillips says to Captain Willard, "you son of a bitch, you f@$". The closed captioning here is wrong and indicates he says "you bastard". (02:22:15)
Other mistake: The soldiers show Captain Willard his new orders, which are visible to the audience. Note there is no mention of Captain Willard anywhere on the page. (00:08:50)
Other mistake: Kilgore watches from the beach after he calls in the napalm attack on Vin Din Dop. We see a large explosion but the three fighters never actually drop any napalm, they just fly over. (00:48:50)
Other mistake: Soldiers are already crashing the stage as Bill Graham gets the helicopter crew to rev up the engines but the two Green Beret security guards that are watching the girls have quite a delayed reaction and act as if nothings happening at all. (01:09:40)
Other mistake: When Chief Phillips tries to kill Captain Willard there's a shot of the captain's back in the bright sunlight. If you look closely at the center of his back below his right shoulder there's a pressure mark similar to what you see on a hot summer day after a person gets up from sitting in a beach chair for a while. On the PBR we see Martin Sheen's character standing for a long time throughout the entire scene, but he was definitely sitting for a while before this particular shot was filmed. The pressure mark is not in the previous shot. (02:23:20)
Other mistake: The map that Harrison Ford points to as Captain Willard recalls back to lunch at General Corman's is an altered prop. The name of the fictitious "Nung River" has been stamped on to the pre existing map of Vietnam using a different colored ink. The actual name of the river can be seen slightly to the left of the stamped in name. (01:18:25)
Other mistake: When we're introduced to Lance on the patrol boat he's sun bathing at sunset facing the wrong way with the sun reflector not reflecting on his face. (00:21:20)
Other mistake: Lance is standing right in front of Chef who is crouching in the sampan. As the melee starts he re-loads his machine gun and proceeds to fire wildly from left to right aiming downward right at Chef who is never hit. (01:36:55)
Other mistake: Lieutenant Colonel Kilgore says, "You smell that? Do you smell that? I love the smell of Napalm in the morning", right after the jet attack and there's no indication that his character isn't smelling exactly what he says he is. There's no way he could possibly smell Napalm in the ten seconds of uninterrupted movie time that has elapsed from the attack. The explosion is several hundred yards away and looking at the smoke canisters, quite a brisk wind is blowing all the smoke away from them and not in their direction. (00:49:15)
Other mistake: As the woman that threw the grenade into the Medevac helicopter runs away they shoot at her from another helicopter. You can see by the puffs of smoke on the ground that the machine gun fire is not going anywhere near her, or her friend running in front of her as they fall to the ground dead. (00:44:30)
Other mistake: The comment about covert missions into Laos where everyone had foreign weapons and uniforms, etc., is bull. Many, many men went into Laos, fully equipped on UH-1A choppers with American gear. The recon teams were outfitted with American gear. I haven't found anyone that could accurately estimate how many, but a lot. A friend that came back from there said they had maps, radios, uniforms, sidearms, fully equipped choppers with rocket rounds, and so many spare barrels and boxes of ammo for the 60s they could barely get off the ground with 4 crew members. No foreign anything in choppers or teams going in or out for any trip. Not saying it didn't happen somewhere during the war, but it was not something that happened in Laos from dozens of combat vets I've talked to.
Other mistake: As Captain Willard gets up, he holds the Schlitz beer can upside down. (00:32:17)
Other mistake: Captain Willard reads to himself from Colonel Kurtz' paper titled, "Commitment and Counterinsurgency". We see a close-up of the page that he's reading from which is fine until he reads, "our conduct of the war will gain only impotence". Everything else he reads is not on the page. (01:15:35)
Other mistake: After we see Chief Phillips break up the fight between Clean, Lance and Chef they show a close-up of the Playboy Bunny's helicopter. It's pouring down but there's no water running off the helicopter or its windows. (01:25:40)
Other mistake: Captain Willard hears the drumming as they approach the USO show at Hau Phat. He's sweating profusely but they don't put any sweat on Chief Phillips, Lance or Clean who, in the same heat, are bone dry. (01:03:15)
Other mistake: Clean gets some tapes from his mom back home but if you look closely at the back of his tape recorder as he grabs it there's no way for him to play the tapes without batteries in it. (01:51:00)
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.