First off - and I haven't like him since Alias - Bradely Cooper is amazing in the role. You can see him as being just talented enough for a woman to try to save and not strong enough for him to let her.
Now. Lady Ga Ga. Wonderful in the first third of the movie. It was really great to see her as a normal person and not someone in a meat dress or whatever. But there is no chemistry at all on her end. SWSNBN thinks it's because in real life she knows Bradely is gay and can't see him as a realistic romantic partner. Whatever the reason she's just like "eh, he gets drunk" and you never ever see her have an expression of passion for him.
Also they introduce her as a woman who can sing with the Eddie Vedder type rockers and write songs like them, but then the movie turns her into a pop star with dancers and shit and essentially makes her Lady Ga Ga. That's a huge mistake. She should have stayed with what she spends the first third of the movie doing and ended up doing the rock thing better than Bradely Cooper.
Finally in the other versions of the film the suicide/not suicide thing is ambiguous. Here it's a clear suicide that he's somehow pushed into my her manager. And that just doesn't work.
But overall? The movie is far better than I expected. I just wish the entire film had been as good as the start.