Continuity mistake: Just before the warrior throws his spear at Chief Phillips there's a shot of Lance at the helm of the boat and we see the right side of the arrow in his hair pointing straight out and the left side pointing upward. In the previous shot both sides of the arrow were pointing straight out. (02:22:25)
Continuity mistake: Chef says to Captain Willard, "We'll go up there, but on the boat, okay?" and you can see orange smoke blowing from right to left across the screen towards Lance. In the next shot of Lance in the water with Chief Phillips' body there's no smoke. (02:24:50)
Continuity mistake: As Chef shows Chief Phillips and Clean the picture in his Playboy magazine of Miss December you can see the USO stage behind them. In the previous shot of the boat leaving one of the six tall lipstick statues on the upper left of the grandstand was knocked down. Now as the boat departs all six statues are standing. (01:11:50)
Continuity mistake: While discussing surfing at the beach party Colonel Kilgore says, "We'll pick your boat up and put it down like a baby where you want it." The cigarette he's smoking here gets longer between shots. (00:33:35)
Continuity mistake: During the napalm attack there's one group of men marching on the other side of the bay. The next time we look over there right after the explosions there are two groups of men marching. (00:48:55)
Continuity mistake: In the first close-up shot of the soldier wounded in the Vin Din Dop courtyard there are two medics working on him. In the next shot there is a third kneeling by his left leg in the exact spot where the cameraman just stood in the previous shot. (00:43:20)
Continuity mistake: When the soldiers lower Clean's body into the grave they're all standing. In the next shot they're all crouching. (02:01:50)
Continuity mistake: After they leave the French plantation Chief Phillips maneuvers the boat through some thick fog and says, "I said I can't see a thing captain I'm stopping this boat, I ain't riskin' no more lives". When he says this line he's looking directly at Captain Willard but in the next shot his head is turned as he looks over towards his right. (02:20:15)
Continuity mistake: The day after the USO Playboy Bunny show, the patrol boat canopy is set afire by some pranksters from a passing boat. Yet, that night in the scene at the Do Lung Bridge, the canopy is intact. It goes through some amazing transformations during the remainder of the picture. (01:41:33)
Continuity mistake: Hubert de Marais continues to speak to Roxanne in French. As she looks at him intently her expression changes and she goes from having her hands at her sides to unfolding her napkin again between shots. (02:04:30)
Continuity mistake: As the soldiers crash the stage Bill Graham ignites the smoke canister and the flashing green running lights above and under the left door of the helicopter are off. In the next shot, as he gets in, they're on. (01:09:55)
Continuity mistake: When Captain Willard climbs onto the top of the boat and again when he shakes Dennis Hopper's hand we see no rips or tears on his green T-shirt. But when he says to Dennis Hopper, "Take who away?" there's a huge rip in his T-shirt under his right arm. (02:29:40)
Continuity mistake: As Captain Willard tries to get Chief Phillips to stop the men from firing he says, "They're just little sticks. They're just trying to scare us". Watch the Captain's left hand closely as his rifle becomes arrows between shots. (02:22:00)
Continuity mistake: As they begin to break out of the fog bank Chef says, "watch it over here, chief, got a stump". Here he's helping Chief Phillips steer the boat with a long pole that he places back on the floor of the boat after the uses it. You can see that it's not hanging over the right side of the boat behind Chief Philips but at the beginning of the arrow attack it's back extending out over the side. Then a few shots later as Captain Willard runs to the back of the boat to stop Chef from firing it's gone completely. (02:20:55)
Continuity mistake: Chief Phillips yells, "Lance, cover the captain" and we can see the shadow of the flag waving behind him on the floor the boat. In the next shot the flag is motionless. (01:57:15)
Continuity mistake: We see a close-up of Lance's face as he talks to Chef on the front of the boat at they approach the Do Lung Bridge. The camouflage makeup around his chin and left cheek is different as he walks across the bridge with Captain Willard. (01:42:35)
Continuity mistake: As the soldiers crash the stage the two rifles that the playmates were using in their dance have disappeared from the stage. (01:09:40)
Continuity mistake: Hubert de Marais says to the Captain, "because life, sometimes is very cruel, as you can see" as he hands him a plaque. At first he's holding it with his left hand then when he gives it to him, he's using both hands. (02:03:15)
Continuity mistake: There have been many shots of the surfboards as they flew to Vin Din Dop and they were all on the skids of the helicopters, now when Colonel Kilgore says, "do you wanna surf, soldier" we see the surfboards placed next to each lengthwise through the helicopter with their fins sticking out the side doors. (00:46:05)
Continuity mistake: Captain Willard shreds all of his notes on Colonel Kurtz and narrates to himself, "but the thing I felt the most, much stronger than fear, was the desire to confront him". In a wide shot of the boat we can see that the flag that covered Clean's body is back on top of the PBR. (02:26:20 - 02:27:50)
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