Continuity mistake: Just before Colonel Kurtz falls to the ground we catch a glimpse of him with blood running from the top of his head down the right side of his face. Several seconds later as the lies on the ground dying there are only a few small drops of blood on the right side of his face. (03:08:05)
Continuity mistake: Clean continues to tell the guys his story and says, "One day the gook took his magazine away from him and wouldn't give them back to him," and Captain Willard's right hand goes from leaning against the machine gun to touching his head between shots. (01:12:30)
Continuity mistake: Dennis Hopper holds his cigarette between the first and second finger of his left hand before he gives the water to Captain Willard in the bamboo cage. In the next shot as he gives him the water the cigarette is between his thumb and first finger. Then in the shot after that it's between his first and second finger again. (02:42:50)
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 the shot shows Chef and his playmate Miss May through the helicopter window it's pouring rain and totally overcast outside. In the next shot from inside the copter, water is cascading down the windows but the sun is now shining. (01:28:55)
Continuity mistake: There's a perfect backlit shot of Captain Willard as he swings at Colonel Kurtz and he's now wielding a third machete as he kills him. This one has a square hatchet like blade attached to a long handle. (03:07:45)
Continuity mistake: During the arrow attack Lance shouts out, "Cut it out, quiet". The boat is traveling straight ahead but 10 seconds later Lance shouts out again, "Quiet" and the shoreline behind him is the exact same spot. (02:21:55)
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: At the end of this scene the shots of Chef and Miss May in the helicopter at the Medevac were done in an entirely different place. All the outside shots of the helicopter have different backgrounds (trees, mountains, tower) from what we saw when Captain Willard first walked around the Bunnies' camp. (01:31:50)
Continuity mistake: As they approach the USO show at Hau Phat, Clean has a very large zit on the left of his chin. Later in this scene as he's speaking to the sergeant about getting some fuel it's gone. (01:03:30 - 01:04:55)
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: As Hubert says, "They put the French army in an impossible situation where they couldn't win." Notice Roxanne and the people next to her, whom are bathed in sunlight, in the next shot the woman has no sunlight on her at all. (02:09:30)
Continuity mistake: Close to arriving to the French plantage, and also when leaving it, Captain Willards' helmet cover changes between a plain olive green and a camouflage.
Continuity mistake: After the 'Valkyrie' helicopter attack, there's a close shot of a soldier who shouts: 'I'm not going.' Another soldier turns back to the chopper to pull him out. Then there is a long shot of the troops at the choppers and you see the same soldier turning back to the helicopter. (00:42:15)
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