I quite enjoyed the movie. Let me tell you what it's about!
I'm a big fan of the Coen brother films, and based on the previews this was a madcap comedy, in the vein of Intolerable Cruelty, Razing Arizona, and Burn after Reading.
But it's not.
Rather, this is a complex film that is much closer to The Man Who Wasn't There, Barton Fink, and (especially) A Serious Man.
So it's actually very in-character for a Coen brothers film. Just not the way the trailers made it out to be.
The movie is very subtle and deeply layered. I'm not going to make you wait for it - the film is about authority. Who has it? How do they get it? Do people give it to them? And if so, why?
This theme is most clearly enunciated during the scene with Baird (George Clooney) and his communist "kidnappers." They talk about the body & the head. The little guy & the boss. It's a bit confusing exactly who is "the little guy" and who is "the boss" - several different perspectives are expressed. But it's generally agreed upon that they are "for the little guy" and presumably represent that angle.
Through the character of Mannix (Josh Brolin) we explore this theme in several ways. On the surface Mannix is "the head" of the studio. He tells everyone what to do, and fixes problems. The studio's body would fall apart without Mannix! But Mannix also has a boss - the offscreen owner of the studio who lives in New York but gets a daily phone call. And Mannix is very serious about his faith - so God (or the church) is also his boss.
We explore the theme of authority through several discussions about faith and diety - most explicitly in the scene in which 4 religious leaders discuss whether the film "Hail Caesar" treats the topic of Christ with respect. Their answers are all over the map - unity is division, division is unity, Christ is God, or a man who is the Son of God, or both, or neither. All four men are pleased though at the mention of Baird Whitlock - because his celebrity gives "authority" to the film's production.
The fictional film-within-a-film echoes this theme again. There is no Caesar in the film - the authority is absent, but felt. The extra playing Christ doesn't know if he is an extra or a principle. Also, the fictional film has the same name as the actual film we watch - so who then is in authority?
At one point, Mannix talks with Hobie Doyle (Alden Ehrenreich) about the kidnapping, and Hobie gives another viewpoint on authority. To him, it's the extras who lack authority - because they aren't invested in the work. Everyone else on-and-off screen is a vital part of the film, but the extras come and go. Mannix reinforces this idea near the end, when he slaps Baird and tells him that pictures have value, and so long as Baird can do work in service of the picture, his actions have value as well.
The resolution of all this questioning - and there is a clear resolution - comes from Mannix's decision about whether or not he should leave Capital pictures (as opposed to Communist pictures?) and take a more stable job doing things "that matter." The question of whether or not work matters (or gossip matters, etc) is another big theme - some people have suggested that it's the central theme. But to me the validation of work is all about authority - so the question of authority trumps it as the main theme.
So by the end Mannix decides to stay - because whether he's the body or the head, he's part of a functioning organism that produces something of merit. And being part of that something is what matters. We all produce work, but we also all create the authority that we serve.