Continuity mistake: After the woman tries to feed Captain Willard some rice he looks to his left and sees Colonel Kurtz standing there with one thin ray of sunlight coming down on his head. We saw this spot in the wide shot when the three soldiers placed the captain near the window and it's in the shade, plus the sun is not coming into the room from above but sideways from the right.
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.
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.
Other mistake: Captain Willard reads to himself from Colonel Kurtz' paper titled, "Commitment and Counterinsurgency". We see a close-up of the page that he's reading from which is fine until he reads, "our conduct of the war will gain only impotence". Everything else he reads is not on the page.