Deliberate mistake: None of the helicopter's in the movie have the Army markings seen on Vietnam era Hueys. The most you'll see is some crooked, faint and inaccurate stencils in the wrong spots. (00:37:50 - 00:51:25)
Deliberate mistake: Martin Sheen has a cut on his cheek that starts as a scar and becomes an open wound. (00:02:27)
Deliberate mistake: After Hubert exit's the French Plantation dinner scene the stage lighting on Roxanne and Captain Willard shuts down abruptly before their close-ups. There's no one there to touch a light switch and we can see outside and the natural lighting hasn't changed. (02:13:30)
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.