Continuity mistake: Kilgore is talking about how he wants to surf the beach. The lighting changes significantly in the space of seconds from the shots of the surf to the shots of the fighting. The shots of the surf are later in the day while the angle of the sun in the fighting shots is higher indicating afternoon.
Continuity mistake: As Colonel Kurtz reads his poetry out loud we see Dennis Hopper gesturing with both hands as he speaks with the captain. When the colonel gets mad and throws the bowl of bananas at them Dennis Hopper is holding his camera in his left hand. His bandana is also rolled up differently with the corner sticking up in one shot and down in the other. (02:56:20)
Continuity mistake: As Captain Willard tries to get Lance away from Colonel Kilgore the band-aid on his right cheek angles upward as it nears his eye. Later we see it up close as they pull him into the boat with the surfboard and it does not angle upward but goes straight across his face. (00:50:40 - 00:51:45)
Continuity mistake: As they depart from the USO show at Hau Phat Chef shows everyone his picture of Miss December and there's a helmet hanging on a poll in the rear of the boat with the top facing Chief Phillips. Each time we see this helmet in the next few shots it moves sometimes facing the back of the boat and sometimes facing the front. (01:11:55)
Continuity mistake: As they approached the French plantation there are two distinct shots of this area, one is from further back then ten seconds later there's a close-up. The clouds in the background are entirely different in these two shots and the clouds change again when the Frenchmen show up. (01:55:50 - 01:59:20)
Continuity mistake: As Roxanne unties the curtains around the bed the scarves draped over the light on the left of Captain Willard are not the same ones we just saw in a previous shot as the captain took a smoke from the pipe. The ones before were red and yellow but now the middle one is primarily green. (02:19:05)
Continuity mistake: On the beach Colonel Kilgore says to one of his soldiers, "what do you know about surfing major, you're from New Jersey" look closely at the Vietnamese prisoners walking on the opposite side of the beach. They're always walking from left to right but several times in this scene they change their starting position from further down the beach (left of screen). (00:45:50)