I would say that my most grievious problem is the way the he conveys internal dialogue, especially when it comes to women like Cersei ad Catelyn, and he's an offender with Jaime as well. Their internal dialogue is just atrocious. The quips and snark and comments the characters want to make but hold back. I greatly detest Cersei and Catelyn, so I can appreciate this just being a piece of their character, but he also does it with Jaime, and with others I can't think of right now, I'm sure. Daenerys, and Aerys Oakhart, as of recent. Sam as well.
Note that I don't have any problems with what he writes
about so much as
how he writes it. Listen, I have no qualms with the blatant, rampant sexism strewn about these books. No problems with it whatsoever. I don't even tolerate it or dislike it; it's part of their world, and as a reader, I accept that. But the way he writes women - completely irrational with so few of them capable of intelligent thought, leaves me no room to relate to any of them. One could make the argument that he's aware of this and even tried to combat this with the strong female characters of Dorne, but so far, even Dorne has fallen short for me. It doesn't come down to sexism. GRRM just does not know how to write women in a way for other women to relate to them*. (*In my own personal opinion as a female reader.)
Another problem is that his writing doesn't jump out at me as overwhelming and profound works of art. That's okay, because they do't have to be. I'm in it for the story and the journey. There are here and there some clever and noteworthy lines, and I'm not expecting to read a literary masterpiece upon every page. Mostly what keeps me going is, as mentioned, what is happening to his characters, not necessarily his own writing. I wish that I
did feel like all of these books I invest in were profound works of art, writing-wise, but it's not how I feel. Still, it's done well enough for me to kick that complaint under the carpet and keep going.
Another complaint, albeit minor, is that I cringe whenever he uses the word "loped" when referring to movement of the direwolves.
It's such an uncommon word, but it's used so often when referring to them and I hate it.