My favorite scene is when Truffaut and Balaban asks the crowd where they heard the notes, and every single arm shoots up and points to the sky. I mean, if you wanted to, you could write an entirely different review about what this film says about the quest for God, and how important that can be to someone of Jewish faith (Spielberg explored the concept with more frivolity in Raiders). Anymore, the aliens strike me as a proxy for all that is transcendent.
You have a very good point about the middle section with his family, which also strikes me as incomplete. But my God, the warmth and hope of that spectacle at the end. It's orgasmic. Truffaut gesturing to the lead alien and smiling is one of THE moments of cinema for me. I'll never forget it.