Yes, it's a movie about making a play, but that's not the kind of drama we're talking about here. Birdman's a film that center's around its characters' struggles to make sense of their lives, and their favorite way to do this is arguing with each other (or their feathery past-selves) about their own purpose and meaning and essentially what it means to be alive and to be successful.
The problem with success is that it's all relative, defined by the success and failure of our peers. So both Riggan and Mike want to use the play to find their own success, all the while Sylvia has a very different definition that involves a little more fathering and a little less knife throwing.
It's a hodgepodge of emotion that drives the film towards its climax.
But for all of the serious, heartfelt confessions and confrontations, there's an equal (if not greater) amount of silliness. We don't want to take the movie joke by joke and ruin them all for you, so let's look at a pretty subtle one that may have flown under the radar (if it still had any feathers).
Yeah, we're talking about the scene where a drunk Mike interrupts Riggan during the first preview and starts tearing apart the set after he's done ripping into the audience. He's pillaging the fridge and notices that everything except a piece of chicken is fake. So he takes a bite decides it's pretty good—as food tends to be when one is inebriated—and he says "That's some good bird, man."
It's really one of those things you need to see first-hand because it will catch you off guard, given the serious nature of the scene. And that's the thing about humor in Birdman: it's all so interwoven into the dialogue of the characters and their ridiculous antics that we find ourselves laughing at them even in their lowest moments.
We're like the people following around an almost-naked Riggan with our smartphones, laughing at his vulnerability.