Biggest problem I have so far is that it is moving pretty fast. I wish there were going to be more episodes so they could take the time to dwell just a little bit on what is going on or being set up. Then there's the acting which is hit and miss for me. Some seem to be spot on and giving it their all, a few seem very stiff and like they're reading a script in their head as opposed to being the character saying the line. Dinklage was great, as was Bean. Viserys got the whiny part down, but otherwise seemed wooden, and Sansa seemed mostly awful. I'm not sure how I feel about their ages all being higher than they are in the books, Caetlyn seems to stand out the most in this regard as she seems about 50 instead of mid 30's.
I didn't care for the changes made to the prologue as I felt they weakened the impact, and didn't like that they showed the guy make a repeated point for the men to get on their horses, and then they never do and are on their feet in the next shot. Seemed a little odd.
Otherwise it showed a lot of potential to be very good, and it should be considering the source material. I'll be hoping they get it right and are able to continue the series through all the books (and hoping the last few books get done in time). Any ideas of what they'll do with the title if they go to more seasons?