Continuity mistake: In the boat Captain Willard reads more about Colonel Kurtz' and fingers through his three Green Beret applications. Right after the captain says, "But when he threatened to resign, they gave it to him," he stops on a prop sheet that had the real names and dates erased and new names and dates typed in using a different typewriter that has darker numbers and letters. (00:01:25 - 01:01:25)
Continuity mistake: When we first see Captain Willard in the movie he's looking at the ceiling fan spinning above his head. There's only one fan above his head yet we see two different fans in the scene. The first ceiling fan has a different motor and the acoustic tiles show signs of water damage not seen on the second fan. (00:01:50)
Continuity mistake: In the beginning of the movie when Captain Willard hears the helicopter flying over and walks to his window the blinds are dark. In the next shot when you see him looking through them they're lit up. (00:04:15)
Continuity mistake: When Captain Willard looks out his window at the streets of Saigon you can tell by the shadows that the sun is overhead. But in the next shot the sun is coming directly through the window and shining on his face. (00:04:20)
Continuity mistake: In a close-up after he burns the picture of his wife with his cigarette, Captain Willard says to himself, "When I was there all I could think of was getting back into the jungle". Look closely at his left cheek and note a red scratch missing from previous shots and not visible in later shots during his drunken dance. (00:05:20)
Continuity mistake: During Willard's bout of insanity in the opening scene, we see him doing karate or something in front of his bed and there's blood visible on the sheets. Yet that is not supposed to be there until he smashes the mirror (half a minute later) with his hand and then runs the blood over the bed and his face. (00:06:03)
Continuity mistake: In the beginning of the movie as Captain Willard dances around his room there's a red and white can sitting on the left of his mirror. It's there for two shots but then in the next shot when he busts the mirror it's not there and we see a box instead. (00:06:45)
Continuity mistake: After he cuts his hand on the mirror Captain Willard rubs his face with his bloody right hand. In the next shot as he attempts to pour a drink into his mouth only his thumb is bloody and there is no blood on his face. (00:07:10)
Continuity mistake: When the soldiers come to the door with Captain Willard's new orders a green piece of paper (money) appears behind his gun lying on the table under the lamp. It's there in the close-up but not when they first walk in. The other pieces of paper in front and to the left of the gun are also moved. (00:08:20)
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)
Continuity mistake: Captain Willard and his two escorts get out of a helicopter and walk up to the guard post on the way to see General Corman. The soldier in the front is carrying some yellow papers in his right hand. In the next shot as they pass the guard the papers are in his left hand. (00:09:40)
Continuity mistake: Before Captain Willard walks into General Corman's residence the front door is in the shade. In the next shot as he walks through it's lit up with sunlight from behind. (00:10:00)
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: In a face on close-up as he talks to General Corman, Captain Willard's scar starts directly under the middle of his right eye. Later at Clean's funeral the scar is shorter and further to the right no longer directly under his right eye. (00:10:30 - 02:00:45)
Continuity mistake: After Harrison Ford lights up his cigarette and walks towards the General, we see Jerry sitting behind him putting the piece of paper he was reading into his briefcase. In the next shot Jerry is holding the piece of paper in his left hand again. (00:10:40)
Continuity mistake: As he speaks to Captain Willard in the general's residence, Harrison Ford lights up a cigarette, leaving a big puff of smoke in the air behind him as he walks away. In the next shot the air is clear without a trace of smoke. (00:10:40)
Continuity mistake: Harrison Ford lights up his cigarette and Captain Willard says, "I'm not presently disposed to discuss those operations sir." Jerry is sitting with his back almost up against the wall. In the next shot as he takes a puff from his cigarette he's moved and is now leaning forward. (00:10:45)
Continuity mistake: As Lieutenant General Corman walks to the table, all of the hutch cabinet doors are closed. 17 seconds later, the left end and right end hutch cabinet doors are open. (00:11:40)
Continuity mistake: At General Corman's they sit down to have dinner and the ID card on his right chest pocket is attached to his shirt differently in various shots. At first it's not even on the pocket then later in the scene it's set right again. (00:11:40)
Continuity mistake: As everyone sits down to have dinner at the General's all the glasses are empty. The next time we see them they're full but no one went around the table filling them. (00:11:40)
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