Continuity mistake: After he hears the Frenchmen shouting at them Chef turns around and looks at Chief Phillips as he puts his gun down on the side of the boat. It in the next shot he's looking in the opposite direction. (01:57:30)
Continuity mistake: As they stand and listen to the Frenchmen shouting at them, the floodlight on the front of the boat, along with the machine gun turret that it's attached to, move about 45 degrees to the left between shots without having any one touch them. (01:57:35)
Continuity mistake: As they listen to the Frenchmen on the plantation dock, Chef picks up his rifle from the side of the boat. Note this spot and the bloody footprints there, which appear and disappear between shots. (01:57:40)
Continuity mistake: When we first see the Frenchmen appear on the dock in the plantation scene there are eleven of them. The next time we see them as Captain Willard approaches there are four and a few seconds later another five more appear out of hiding. (01:57:55)
Audio problem: On the French plantation dock Captain Willard walks over towards the Frenchman and they do an excellent job of overdubbing the sound of his helmet strap each time it hits his chest. Two shots later they don't put in the sound as the helmet strap hit's against his chest several more times. (01:58:00)
Continuity mistake: They took the flag from the PBR (which is removed from the roof of the boat the next time we see it) to cover Clean's body at burial. It's not the same flag, the last red stripe on the bottom of the PBR's flag is torn off as we see at the French Plantation dock. The flag on Clean's body has the last red stripe and also has a shorter white stripe on it's bottom. There's no indication that there is more than one flag on the PBR (redux version). (02:00:05)
Continuity mistake: When the soldiers carry Clean's flag draped body to its final resting place there's no sunlight from behind falling on the flag. The next time we see it it's bathed in sunlight coming from the opposite direction. (02:00:30)
Continuity mistake: When the soldiers carry Clean's body to it's grave his head and feet are not covered. The next time we see him they are. The cords tied around his body are also in a different position. (02:00:35)
Continuity mistake: Clean's burial is two minutes of uninterrupted action. When they first carry him over he's on a bamboo stretcher. One of the soldiers proceeds to take the flag off of him then another puts it back on. When we see his body again a few seconds later the flag is in exactly the same spot but the stretcher underneath is gone. (02:00:45)
Continuity mistake: As they carry Clean's body to the grave there's a lot of smoke blowing through the area. The smoke is in each shot except the close ups of Clean's flag draped body when there is no smoke at all. (02:00:50)
Continuity mistake: As they prepare to lower Clean's body into his grave Lance stands to his right and reaches down to lift the flag. According to his wrist watch it's 11:45 but twenty seconds later there's a close-up of Chief Phillips' watch and it's now 4:10. (02:01:10)
Continuity mistake: At the funeral Chief Phillips picks up the flag from Clean's body holding it between his fingers about two inches in on each end. In the next shot he's holding it on the edges and the flag is reversed with the stars and stripes on the right. (02:01:15)
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: In the first shot of them having dinner at the French Plantation a Vietnamese waiter speaks to the woman at the right of the table. In the next shot he's speaking to the man sitting next to her. (02:02:40)
Continuity mistake: In the second shot of dinner at the plantation a French boy is speaking to the people seated at the table. There's no centerpiece or flowers in the middle of the table but there is in the next shot. (02:02:50)
Continuity mistake: As the little French boy goes to kiss Hubert de Marais the man wearing a tan jacket in the center of the screen goes from looking to his right to looking at his food between shots. (02:03:00)
Continuity mistake: After the little French boy kisses Hubert de Marais he walks away and we watch from behind as Captain Willard's head turns to the right as he looks at him. In the next close-up of the Captain's face he does the exact same thing again. (02:03:05)
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: As Roxanne sits down at the table Captain Willard looks at Hubert de Marais. In the next shot he's smiling and looking at Roxanne. (02:04:10)
Continuity mistake: After Roxanne sits down to the eat she says something sweet in French that makes Hubert de Marais chuckle, and also makes the amount of wine in his glass decrease between shots. (02:04:25)
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