I would like to start by saying that I have read A Game of Thrones and A Clash of Kings and so far, I absolutely love A Song of Ice and Fire. I love the huge cast of characters, and the intrigue, and how Martin isn't afraid to be unflinchingly cruel, to the point where I actually believe that no character is safe. I love Arya Stark, and I want to have Tyrion Lannister's babies. If either of them dies (don't spoil it, please!) then I will go lock myself in my room and mourn for the rest of the week.
Also, this post contains un-hidden spoilers for both books, so if you haven't read or watched the first two books/seasons, then you might not want to read this.
With that said, there is something that may or may not be problematic about the series: its representation of female characters. Let's consider all of the major female characters in the first book, A Game of Thrones:
-Catelyn Stark: Devoted mother and wife, but also intelligent, brave, and practical. Probably the most positively-depicted female character in the series.
-Sansa Stark: The girly-girl. She's loves pretty things, romantic stories about knights, and is obsessed with Prince Joffrey. She eventually grows more disillusioned over the course of the first two books.
-Arya Stark: The tom-boy. She can hold her own in a fight and isn't bad at underdog strategy.
-Daenerys Tagaryen: Starts out in a position where she is brainwashed and forced around by her brother and the other men around her, but grows into a strong and capable leader.
-Cersei Lannister: The femme-fatale. Pretty, manipulative, and cold, but also a mama bear when it comes to protecting her children.
-Lysa Arryn: Paranoid and kind of insane.
Out of all of these characters, only three are generally positive: Catelyn, Arya, and Daenerys. Considering that they represent half of the characters listed above, that's not a bad ratio. (Not to mention that ASoIaF has no shortage of male characters who are weak, stupid, arrogant, manipulative, traitorous, or cruel.) However, Daenerys is very much at risk of slipping to "villain" territory. She has been raised to believe that her family is the true line of kings and that Robert stole the throne through savage cruelty (which is not entirely untrue.) Therefore, it is her duty to reclaim the throne. Even after Ser Jorah Mormont explains to her that the people don't really care who is king--they just want to be left alone (and she acknowledges that he has a point), she doesn't back down from her quest to reclaim the throne. (Not an entirely wise course of action either, considering that she won't have any heirs.) I just hope that she manages to stay sympathetic (and alive, please!) throughout the course of the books.
It's hard to say whether Sansa is a "positive" character or not. Throughout most of A Game of Thrones, she is naive to the point of stupidity--which is somewhat forgivable, considering that she is only eleven years old. (Although the actress they cast to play her in the television series is well into her teens, which makes her a lot less sympathetic.) She does have some moments of capability, like when she negotiates for her father's life, but for the most part, she is very much a damsel-in-distress. (Also, she's bad at math.) I hope that she goes on to play a more active role, rather than remaining a victim to the status quo.
So basically, the only unquestionably positive female characters are Catelyn and Arya. However, since Arya acts like a boy and rejects anything feminine, it's difficult to call her "a positive depiction of femininity." One criticism of modern feminism is that in order for a female character to appear "strong," she has to essentially act like a man (see this video by feminist vlogger Anita Sarkeesian). I really hope that this series doesn't continue to put out that message. So in that sense, Catelyn is the only character who is unquestionably an example of feminine strength.
Overall, I think George R.R. Martin's female characters are much more developed than in several other media that I can think of. And for that reason, I would like to continue to see more than damsels-in-distress, femme-fatales, and women who have no personality whatsoever. I look forward to reading more into the series (and of finding a way to watch the TV series without having to pay a ton of money), and I really hope that I don't come out disappointed.