From what I understand, most people's criticism is with the heavy handedness of the delivery of the political allegory underlying the discourse of the film.
Firstly, I find it ironic that people mention the movie's lack of subtlty, because after reading several depraved rants from keyboard warriors and arm-chair "critics" it still seems that no one actually completely understood the film! Even with the aforementioned allegorical hand holding done by Andrew Dominik in his (superb) direction and screenplay, viewers still can't/won't engage with the film on its own terms.
The allegory needed to be made and it needed to be clear from minute ONE. Why? Because that is where the REAL STORY IS and Dominik wants you to know that. He also wants you to know that the economic collapse of 2008 was far too affecting on the lives of Americans to be thrown subtly into the background. This event was a chain reaction that affected EVERYONE from ALL CLASSES. What the audience is seeing is how those at the bottom of the social class deal with this INSTEAD of the upper/middle class viewpoint. The characters are among the lowest form of human life, but it serves to remind us that these types of people exist and that they're fighting it out and struggling to get by (and just get "fuckin' paid") in a world that has completely abandoned them. These are not the people waiting for "CHANGE."
Driver (Richard Jenkins) remains nameless which serves as a clue to his allegorical representation in the film. Most likely he represents the Government: They know there's a problem and when a clear solution comes to them (in the form of Brad Pitt's character Jackie Cogan, who represents the voice of reason), they remain indecisive because they don't want to upset anyone on 'the board' (Corporations, etc. who fund party campaigns and bribe politicians to influence the political process). Driver neglects the harsh truth of the sitution, while Cogan brings it to the forefront, "Put him out of his misery." I guess in a way, James Gandolfini represents a lamenting wall street broker who was really good at his job for a time and has now hit rock bottom. His work has finally caught up to him (the stories he tells Pitt are an example of this and these can be met with either sympathy or anger) while still indulging in the same narcissistic pleasures he had while 'on top' without hesitation.
It's cynical. It's angry. It's berating. It's unabashedly anti-american. It's hard hitting. I can understand the hate for the film coming from patriotic Americans, viewers/critics with strong political values and audiences who were expecting a thrilling gangster film with explosions, shoot outs and Brad Pitt kicking ass. So far I've yet to see many people here on RT putting forward a sensible and reasonable argument that condemns the film for not achieving its aims. To me (and to all viewers who complain that Andrew Dominik bashes the viewers over the head with political allegories) it achieves exactly what it sets out to do as outlined above.
Lastly, I'm rather dismayed by those that encouraged RT users to request that cinemas ditch the screening of the film because it didn't align with their preconceived expectations of the film. I understand this isn't the 70s anymore and a lot of people align their cinema experience toward the entertainment spectrum, rather than an artistic medium challenging the social norms of the time. Still, I think people need to be a little more respectful of other people's viewing habits, instead of assuming everybody's view aligns with their own.