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: When Willard has a severed head dropped on his lap, the stump is clean and flat like it was sliced by a samurai sword. When the head falls to the ground, the stump is bumpy and ragged like it was hacked with an ax.
Continuity mistake: Close to arriving to the French plantage, and also when leaving it, Captain Willards' helmet cover changes between a plain olive green and a camouflage.
Answer: It's not any specific song; it's just the kind of generic piano music you'd hear at dinner at a high-class restaurant of the era. Think of scenes in movies, films, etc. set or made in the '50s and '60s, where the characters go to a nice dinner and there's someone at the piano playing unobtrusive music to accompany the food/conversation.