I was watching the TNG episode "Lessons" and I noticed that Picard's hands change when he first plays the duet with Daren. In SD on Netflix it is obviously so fake looking. I'm surprised they didn't try harder.
Are you watching this on blue ray? Its been a while since I've seen it on regular dvd, but even then it was obvious Picard was miming to an off-camera or post addition. I recall reading that the actual flute didn't even work as a flute but allowed him to blow into it to help the illusion.