Continuity mistake: The first time we see the severed heads there's a lot of white dry ice-like smoke to the right of Dennis Hopper. The next time we see this spot several seconds later the smoke is just starting to appear. (02:33:20)
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: As Chef and Clean have a verbal fight after they leave the Medevac Lance is in the front of the boat putting on camouflage while holding a mirror in his right hand. In the next shot he's leaning on his right arm and holding the mirror in his left hand. (01:33:20)
Visible crew/equipment: Captain Willard says he made a deal with the playmates for all the guys and Chief Phillips says," you got some mama's in there?". You can see all the stage lights reflecting off their raincoats. (01:27:10)
Continuity mistake: In General Corman's residence Captain Willard walks past the dinner table and there's an extra light green plate between his plate and the chair that's not there later when he sits down for dinner. None of them went near the table. (00:10:20 - 00:11:40)
Continuity mistake: At Kurtz's compound Lance sits at the front of the PBR watching them chop down the dead body hanging from the tree. The machine gun behind him rotates 45 degrees counter clockwise between shots. (02:34:30)
Continuity mistake: As the captain smokes his cigarette Dennis Hopper says " but he's got something in mind for you, aren't you curious about that". The bloodstain on the bamboo pole to the left of the captain disappears between shots. (02:43:25)
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: 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)
Continuity mistake: In the first shot of them having dinner at the French Plantation a Vietnamese waiter speaks to the woman at the right of the table. In the next shot he's speaking to the man sitting next to her. (02:02:40)
Continuity mistake: As they pull Colonel Kilgore's surfboard into the boat it's sitting sideways on the railing of the boat. Then in the next shot the tail fin is back in the water. (00:51:30)
Continuity mistake: There are four shots of the fighters that drop the napalm. The first time we see the jets there's only three of them and the part of the nose in front of the cockpit is painted black. The second time we see them there are five planes, the third time we see them there are four without black paint and the last time we see them there are three. (00:47:55 - 00:48:45)
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)
Continuity mistake: On the boat after leaving Kilgore Chef lights up a joint and hands it to Lance who holds it between his thumb and index finger. In the next shot it's between his 1st and 2nd fingers as he offers it to the Captain. (00:52:25)
Continuity mistake: As the men walk on the shore looking for Colonel Kilgore there's a field behind them across the bay. There's only a tank there but in the previous shot as they landed there were four helicopters along with the tank. (00:25:30)
Continuity mistake: When Colonel Kilgore leans down to give the VC soldier a drink from the canteen watch closely as the roses on the rosebush to the left of the injured soldier disappear and then reappear between shots. (00:29:25)
Continuity mistake: Chef says to Miss May, "You're beautiful, I just want to " and a white Styrofoam ball appears stuck in her hair between shots. (01:30:25)
Visible crew/equipment: As they sit in the foxhole watching the surfers, Lance's helmet gets wet and you can see the reflection of two studio lights, and the crew standing between them, in it. (00:47:10)
Continuity mistake: Colonel Kilgore walks away from his helicopter saying, "Body cards, bring my body cards." Behind him is a radioman and an antenna that is kinked at a 45 degree angle. Two shots later the antenna is standing straight up without adjustment. (00:27:10)
Continuity mistake: When Captain Willard punches the mirror with his right fist, he bloodies it up considerably. Later in the scene when the soldiers come and throw him into the shower, we see a close-up of his right hand without any cuts or blood. (00:09:15)
Chosen answer: Kurtz was protected by political connections and his military record from being relieved of command, and the Montagnard people whose village he was in were considered American allies, so they couldn't just send a force in to kill him or relieve him of command, but an individual assassin. (The US Government's "official" policy is that they do not engage in assassination, which is why "this mission does not exist, nor will it ever exist").
Captain Defenestrator