Arya has the possibility to become super interesting, in kind of a reverse Jaime way. I think her biggest problem has been seeing the world in terms of black and white. She's at an age where she hasn't yet developed a good sense of the grey areas. Part of that is being Ned Stark's daughter, but it's also her being immature. She carries a lot of hate and instead of being healed of it, I think she will be driven to commit acts that force her to develop this sense of grey morality that she has been missing. I think she will still have that strong sense of right and wrong, but will have to learn that it's not always so simple.
She gets angry at Sansa for lying. Yes, Sansa was stupid for that, but she was also put in a delicate position. She was brought before the king and asked to call his son a liar, something Ned tried to teach Arya, but she just couldn't understand. She hates the Hound for killing the butcher's boy, but refuses to see that there is potentially some good in there. She gets upset with the Brotherhood for selling Gendry because she can't comprehend that it's possible they sold him both for the gold and for their god. And now she's in a position where she will probably have to do some very questionable things if she hopes to survive. Then there's the issue of her saying she doesn't want to grow up to be a lady, but she sure slips into that role pretty easily when she needs to get back into the castle after she gets back from chasing cats. "I'm Arya Stark of Winterfell, let me in or my father, the hand of the king, will throw you in a dungeon!" or something like that. Arya's story moving forward can become soooo fascinating because we get to watch how she develops. PLUS there's this little nugget my friend gave me about season 1: Robert says to Ned "I have a son, you have a daughter, we'll join our houses." Well, it seems that Gendry didn't want to stay with Arya because she'd always be high born and he'd be a big nobody from the slums. Well he just found out he is Robert's son! And Arya is Ned's daughter! Future love connection?! Who knows. AGBDSKJGNGJDS I'm excited to see where Arya goes now.