All of the performances were exceptional; particularly Carey Mulligan's, but Cooper is also fantastic. Plus, to play this role and direct a film like this at the same time is undeniably impressive. The score is all source recordings of Bernstein's original compositions or conducted works, and it all works beautifully. Likewise, the cinematography, by Matt Libatique, is also very good and captures many different eras from the 30s/40s to the late 80s perfectly. I have almost nothing but praise for everyone involved here on the production side.
Unfortunately, with all that said, I think the film has a few story issues.
First, as a biopic, it tries to cover a massive span of Bernstein's life, which necessarily means that the film is told almost entirely through brief scenes and vignettes that go by super quickly. Also as a result of the expansive chronology, the film takes gigantic leaps forward in time, which means most scenes barely connect to each other at all. This creates uneven pacing and some jarring macro edits that make it a little hard to follow and which more importantly make it difficult to get to know anyone on a deeper level.
I think it would have been wiser to shrink the narrative to a pivotal time in Bernstein's life rather than trying to cover basically 50 years all at once.
Secondly, the film focuses almost entirely on Bernstein's relationship with his wife Felicia and his various gay romances, at the expense of paying any serious attention to his music or his process as a composer and conductor. Granted, as someone who spent years in music school learning how to compose and conduct myself, I may be biased here, but I'd have really loved to spend more time with Bernstein the musician.
We just don't get a lot of that, even though whenever we do get to see Cooper in that role, he's really good. Most actors who try to conduct on screen are a disaster. Cooper clearly put in the work... But there's only a couple scenes where it actually matters.
And frankly, Bernstein isn't (and shouldn't be) remembered for his sex life, but for his immense contributions to the musical arts. Seems weird to not make that the center of the film.
In the end, it should definitely be an Oscar contender in acting, cinematography, and producing... But its writing and editing are much weaker than I'd have hoped.