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: As Dennis Hopper and Chef walk away Lieutenant Colby towards the severed heads when Chef says,"He's gone crazy!" note Hopper's hands move from his sides to raised in one cut. (02:33:30)
Continuity mistake: As they approach the severed heads Dennis Hopper says, "Wrong, wrong, if you could've heard the man just two days ago". The lock of hair falling over the left side of his bandanna is combed differently between shots. (02:33:35)
Continuity mistake: When Dennis Hopper says, "The heads, you're looking at the heads, sometimes he goes too far, he's the first one to admit it" look at the two cameras around his neck. At first the lenses are both pointing outward then in the next shot he turns around and the left camera lens is pointing at the ground. (02:33:40)
Continuity mistake: Dennis Hopper and Chef are looking at the heads on the ground, Chef turns to face him as Hopper says, "You were gonna call him crazy?" In the next cut Chef is looking forward at the heads again. (02:33:40)
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: While sitting in the PBR at Kurtz's compound, Chef and Captain Willard discuss what they should do as the Captain puts on a clean shirt. Chef says to him, "He's wacko man. He's worse than crazy, he's evil." The background (box behind captain's head) changes. (02:34:40)
Continuity mistake: As they sit in the boat at Kurtz's compound discussing what they should do, Captain Willard tells Chef about the air strike and hands the radio to him with the antenna standing straight up. In the next shot as he grabs it the antenna is folded over. (02:35:45)
Continuity mistake: When they first meet, Colonel Kurtz says to Captain Willard, "Have you ever considered any real freedoms?" and the Captain's shadow appears on the stone column to the right of the Colonel. The Captain is kneeling down and hasn't moved from his spot, but when we saw this column before his shadow was not anywhere near it. (02:39:25)
Continuity mistake: As Dennis Hopper walks up to the bamboo cage where Captain Willard is being held, a purple haze surrounds them. In the next shot when Dennis hopper gives him a drink of water the purple haze is gone. (02:42:40)
Continuity mistake: As Dennis Hopper gets the captain some water we see a wide shot of five bamboo cages with a guard standing between them. In the next shot as Dennis Hopper turns around from the fountain the guard is facing the opposite way and is now talking to the prisoner in the cage that was on the left (now behind them). (02:42:45)
Continuity mistake: In the close-up of Dennis Hopper giving the Captain some water he holds the ladle between his first and second finger. In the next shot he's holding it between his thumb and first three fingers. (02:42:45)
Continuity mistake: Dennis Hopper walks up the steps to the bamboo cage where Captain Willard is being held and gets some water from a fountain about five feet to the right of the cage. In the next shot as he turns around the cage is right there next to him. (02:42:45)
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 he gives the captain some water Dennis Hopper says, "Why would a nice guy like you want to kill a genius?" The tip of Dennis Hopper's right ring finger is black with soot. In the next shot the soot is not there. (02:42:50)
Continuity mistake: The cigarette that Dennis Hopper hands to Captain Willard is lit and in perfect shape, however in close-up the cigarette is bent near the filter. In the next shot it is once again in perfect condition. (02:43:20)
Continuity mistake: Dennis Hopper says to captain Willard, "the man really likes you" as he hands him the cigarette. In the close-up look closely at Hopper's right hand, as a cut appears on his forth knuckle that wasn't there in the previous shot. (02:43:20)
Continuity mistake: As he talks to him in the bamboo cage Dennis Hopper gives Captain Willard a cigarette with his fingers outstretched. In the next shot his fingers are clenched in more of a fist. (02:43:20)
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: The blood and scrapes on Captain Willard's nose disappear as he speaks to Dennis Hopper from the cage. (02:43:30 - 02:45:00)
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