Continuity mistake: When Chief throws the binoculars to Captain Willard, Clean puts on his flak vest. 7 seconds later, Clean is not wearing the flak vest, then he puts it on again. (00:24:37)
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: After Captain Willard smashes the mirror, there is no blood on his right hand and chest. 5 seconds later, there is.
Continuity mistake: After Clean is killed, the blood splatter on the PBR's metal plate changes. (01:52:34 - 01:52:58)
Other mistake: As Captain Willard gets up, he holds the Schlitz beer can upside down. (00:32:17)
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