I guess he watched a lot of Titanic out of the movie archives from his local library when he wasn't serving tea to his "father" and creator. I wouldn't have thought that would have been a favorite of his though. He seems to be into the intellectual movies and music from watching Prometheus. A:C makes me think the same too.
His flute playing is a little anemic without the orchestra as well.
Also, David is crazy and does not love Shaw. He only thinks he is because he has seen what humans do when they do love one another. David is just good programming gone wrong
This is a fake video since I don't think David would be playing wrong notes while playing a song in memory of Shaw (because he doesn't love her).