Other mistake: Lieutenant Colonel Kilgore says, "You smell that? Do you smell that? I love the smell of Napalm in the morning", right after the jet attack and there's no indication that his character isn't smelling exactly what he says he is. There's no way he could possibly smell Napalm in the ten seconds of uninterrupted movie time that has elapsed from the attack. The explosion is several hundred yards away and looking at the smoke canisters, quite a brisk wind is blowing all the smoke away from them and not in their direction.
Continuity mistake: Captain Willard says, "Whatever was going to happen, it wasn't gonna be the way they called it back in Nha Trang". Note the light pole in the center of the boat, the second blue light from the top is shot out however there hasn't been any battles since the French plantation scene when all four blue lights were intact.
Audio problem: On the boat while reading Kurtz' file Captain Willard narrates to himself, "dear son, I am afraid that both you and your mother well have been worried at not hearing from me during the past weeks, but my situation here has become a difficult one". At this point they show the actual letter that he's reading from and the text of the letter is not the same as what we are hearing.
Continuity mistake: In the boat Captain Willard reads more about Colonel Kurtz' and fingers through his three Green Beret applications. Right after the captain says, "But when he threatened to resign, they gave it to him," he stops on a prop sheet that had the real names and dates erased and new names and dates typed in using a different typewriter that has darker numbers and letters.
Continuity mistake: In the scene where they stop the junker boat that they think might be smuggling supplies, as you watch the many scene angles, you can tell that the sun is at different points at different times. Where Willard is sitting at the side of the boat the sun is nearly set, and at one point is below the horizon. At another time, you can tell, the sun is several degrees above that, and in one angle, it is practically noon. Also, the boats change angles, toward the shoreline, possibly to shoot a scene from a better light angle.