Continuity mistake: As Hubert de Marais explains, "The French officer mentality," to Captain Willard, Roxanne goes from looking at the waiter on her left to looking at Hubert on her right between shots. (02:05:15)
Continuity mistake: The gentleman in the tan jacket to the left of Roxanne is eating when Hubert says, "You don't understand our mentality". In the next shot he's reaching over and pouring a glass of wine for her. (02:05:20)
Continuity mistake: During dinner Hubert de Marais starts to rattle off all of the places in the world the French have lost wars. In the next shot the wine glass in front of Captain Willard goes from one quarter full to three quarters full between shots. (02:05:30)
Continuity mistake: Hubert de Marais says to Captain Willard, "And this is something that you never understood, you American". The gentleman in the tan jacket to his left lowers his cigar towards the ashtray. In the next shot his hand is resting on the table with the cigar between his fingers then he puts it in the ashtray. (02:06:50)
Continuity mistake: The old gentleman sitting across the table from Hubert de Marais says, "Maybe in the future we can make something with the Vietminh" and the gentleman to the left of Roxanne replies, "Don't you understand". If you look closely the cigar that he just put into the ashtray in the previous shot, along with its smoke, has disappeared. (02:07:00)
Continuity mistake: In a shot from behind his head Captain Willard sits and looks at Roxanne as the man in the tan jacket to the left of her says, "Look, Captain". In the next shot the captain's right hand is raised shielding his eyes from the sunlight. (02:07:15)
Continuity mistake: The gentleman sitting next to Roxanne in the tan jacket gets up and says, "Look, this is the truth, an egg, the white left, but the yellow stays". If you look closely the lazy Susan in the center of the table holding the oil and vinegar has been rotated between shots without being touched by anyone. (02:07:20)
Continuity mistake: The gentleman sitting next to Roxanne in the tan jacket gets up and says, "Look, Captain," and Roxanne reaches over with her right hand as she holds her cigar in her left. In the next shot she's sitting with both hands on the table and the cigar in her right hand. (02:07:20)
Continuity mistake: The gentleman in the tan jacket sitting next to Roxanne says, "Look an egg" and the glass in front of him fills up between shots. (02:07:20)
Continuity mistake: After the gentleman in the tan jacket says, "The white left, but the yellow stays". Look closely at the plate that he drops the egg into as the two pieces of bread change into pastry between shots. (02:07:25)
Continuity mistake: After the gentleman in the tan jacket spills the egg into the plate, between shots Roxanne goes from having her right hand on the table to having her right hand near her mouth holding her cigar. (02:07:30)
Continuity mistake: The Frenchmen with the accordion asks Captain Willard, "Do you know anything about Dien Bien Phu?". If you look closely at the doors in the other room, most of the lower shutters are closed. The next time we see them all as the Frenchman playing the accordion stands behind the captain and says, "Dien Bien Phu, okay" all the shutters are open even though no one goes near them. (02:08:30 - 02:10:00)
Continuity mistake: The entire French plantation dinner scene is beautifully lit. It looks as though it's sunset until Hubert walks over to the window in middle of the scene. As he stands by the window we can see outside and it's not sunset but midafternoon. Then as he walks to his seat he passes back into the yellow stage lighting again which makes it look as if it's sunset. (02:08:50)
Continuity mistake: As Hubert stands at the window he says, "The generals and the colonels believe it's impossible for the Viets to get the cannons up there in the mountains". It's clear to see that all the windows are closed but the next time we see them the second one from the bottom is open even though no one has gone near them. (02:08:55)
Continuity mistake: As Hubert says, "They put the French army in an impossible situation where they couldn't win." Notice Roxanne and the people next to her, whom are bathed in sunlight, in the next shot the woman has no sunlight on her at all. (02:09:30)
Continuity mistake: At dinner, the Frenchmen sitting to the right of Captain Willard says, "Why don't you Americans learn from us, from our mistakes?" When he says this there's a shadow falling on his face but in the next shot his face is lit up again by the sun. (02:10:10)
Continuity mistake: The Frenchmen playing the accordion walks away from Captain Willard into the other room and trips over something. Look closely at the table because two shots later everything will be different. The fruit in the fruit bowl is entirely different, the flowers and the lazy Susan have been moved and some of the wine and water in the glasses are at different levels. (02:10:15)
Continuity mistake: Hubert has a discussion with the Frenchmen sitting to the right of Roxanne who gets up and leaves. As he gets up his hands are on table but in the next shot they're at his sides. (02:11:05)
Continuity mistake: Hubert says to Captain Willard, "We took the Vietnamese, work with them, make something" and the guy sitting on the right of Roxanne who got up and left several shots ago is back. (02:12:15)
Continuity mistake: Roxanne prepares a pipe for Captain Willard and says, "It was the morphine he took for the wounds he suffered in his heart." The shadow of her left hand falls on her face as she holds the needle over the flame. In the next shot, however, the lighting has changed and the shadow is now nowhere near her face. (02:16:40)
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.