Character mistake: After Captain Willard walks through the front door of the burnt out French plantation dock there's a close-up of Chief Phillips at the wheel the boat. He turns around and looks right at Chef and says, "Lance". (01:56:40)
Character mistake: When Colonel Kilgore is handing out death cards to the dead VC he says, "eight of spades". If you look closely at the card that he throws as it flies threw the air it's the six of spades. (00:28:00)
Character mistake: When Martin Sheen is on the boat, looking over Col. Kurtz's school papers, there is a dissertation by Kurtz on the history of the Philippines until 1905. The word Philippines is spelled "Phillipines"
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 could go in. (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