Continuity mistake: When the soldiers come to the door with Captain Willard's new orders a green piece of paper (money) appears behind his gun lying on the table under the lamp. It's there in the close-up but not when they first walk in. The other pieces of paper in front and to the left of the gun are also moved.
Continuity mistake: As Colonel Kurtz sits and reads articles to Captain Willard from Time magazine look very closely at the clasp of his dog tag necklace on the left of his neck. Throughout the shots he keeps both hands on the articles that he's reading yet the clasp on his necklace moves down his neck more than an inch without being touched.
Continuity mistake: At the dinner table General Corman tells Harrison Ford to, "Play that tape for the captain please" and we see a close-up of his watch and it reads 4:37. It's late for lunch but when Harrison Ford brought the can of Budweiser to the general it was lunchtime as his watch read 12:35.
Continuity mistake: Right after the napalm explosion there's a wide shot of the beach as Colonel Kilgore and the two soldiers with him look across at the destruction. We also see Lance sitting alone in the crater and Captain Willard is nowhere near them. They cut away to the PBR for three seconds then back to the crater and the Captain is sitting next to Lance again.
Continuity mistake: As Captain Willard sits in the boat looking at pictures of Colonel Kurtz the shadow of a metal bar slowly goes from left to right across the pictures indicating that the boat is turning. In the next shot of Clean dancing to Satisfaction we can tell by looking at the sky that the boat is not turning but going straight ahead.