I just saw this today. Hot damn this was just intense, a feat considering it was neither an action nor suspense thriller type of film. I couldn't help but just absolutely buy into the emotional rollercoaster ride of the music student that Miles Teller experienced. I used to play music competitively, although I never went to a music school, but I could still definitely relate to the characters and the competitive nature of everything that was going on—like how Miles Teller's character was so driven & obsessed with succeeding, "showing up" to a demanding teacher, aspiring to become as good as his peers, etc.
The best way I can describe JK Simmons' performance: a tour de force of anger and intensity, with both inner & outer emotions. And every time he got mad, you could feel his anger pouring off the screen. The first time he threw something I totally flinched and froze up.
Really quite an amazing film that was incredibly well-directed and well-made, and took advantage of the fact that it was also about "music" (modern jazz specifically). That last continuous no-edit-gaps musical number with the ensemble was something I hoped the film would end up doing and it totally delivered the best kind of barrage musically and in terms of acting! JK Simmons totally deserves the Oscar, and IMO, so does the film. Easily one of the best things I've ever seen of all-time, not just last year.
I think this film, Birdman, and The Grand Budapest Hotel together form a trifecta of some of the most genius filmmaking of 2014, and I won't complain if any of them win the Best Picture Oscar, but I
will complain if none of them don't.
Besides the obvious greatness of the entire film and the performances, can we talk about how great the dialogues are too?! I was alternating between almost having an anxiety attack and laughing at some of Fletcher's lines ("Are you one of those single tear people?!", "I can still see you Mini-Me!") 
