It's interesting that the first comment I read on this board (just finished watching the movie), which is yours, mentions Hathaway's looks, and not only her performance. I've always liked that actress despite her questionable career choices, and I became pretty fond of her since Les Misérables, because with that movie, she finally showed us how brilliant she can be, AND she cut her hair ! Well, in Les Miz, it wasn't sexy at all, but without it, Hathaway might have never tried that haircut, which would have been a shame, because to me, unlike most actresses, short hair fits her better than long hair. And in Song One, boy... I was totally hypnotized by her beauty. The fact that she acted so well and was so moving in a lot of scenes made her even more gorgeous, without a doubt. As you say, she can do more with her eyes than a hundred pages of dialogues... I think it's her big über-expressive Disney eyes. Anyway, she's slowly turning into one of the best actresses in Hollywood, right now (she's awesome in Interstellar). I wish she'd be more present (if she could trade places with Keira Knightley, it would be nice...).
Actually, I think Hathaway nearly made the whole movie. Song One is not bad, as you say, it's quite charming... but it also very minor. As a movie about music set in New York, Begin Again did a better job a few months ago, the songs were just okay (and I like Jenny Lewis a lot), there was a lot of chemistry between the two leads but their romance lacked originality and climax, and the directing was very indie movie 101. It almost feels like the director knew it, and relied on Hathaway's aura, putting her in every scene, messing with her hair...^^ it makes the movie look like a 90 minutes showcase of Anne Hathaway.
But it was nice, still. Loved most of the scenes in the hospital room. And the fact that they shot in actual Morocco.
"If it's any consolation, fish aren't never even really alive. They're just less dead."
I have to agree that begin again was a much better movie. The songs from Begin Again are so catchy I often find myself humming them and I watched the movie several times, because parts of it were so brilliant and poignant, and mainly because the songs are so good.
Song one, on the other hand, had an awful song showcase. Song One began with great promise but by the time It got to the end I was already tuning out. All I could think when Henry did wake up was "If she keeps shaking him like that he is going to go back into a coma - Noooooo!" because then the movie might never have ended...