Bran is learning to become a greenseer. He can already do skin-changing/warging/posessing the bodies of most animals. Greenseeing seems to involve being able to see at any distance and even into the past. Into the future? I don't think so.
The three-eyed-crow man used to be called Brynden before he wandered into a cave beyond the wall and became one with a tree. That's quite a Stark name. Or is it a Tully name? Was there a Brynden Stark or Tully who went missing a long time ago?
Bran keeps posessing Hodor and is keeping it a secret from everyone. It's a bit weird and no good can come of it, I'm sure. Bran is in love with Meera and even at one point considers using Hodor to comfort her when she is upset about her brother.
Speaking of Jojen, he's not doing much, seems a bit depressed, wants to go home, but isn't. And he's having green dreams but I'm not sure what they're about, but they are what is upsetting Meera.
The Children of the Forest call themselves "those who sing the song of the earth". They live for hundreds of years, and when they die they store their memories in the trees. GRRM has been watching Avatar, hasn't he? The singers have been living in these caves for a million years. There are holes in the caves that go to the centre of the earth. Bran had better watch out for balrogs! The singers taught men how to use ravens to send messages, except that back in the day they used to speak the messages instead of having them written down and tied to their feet. I'd like to know more about the ravens. How do they know where to go? Or are they like homing pigeons, in which case once all the ravens are "home" presumably someone has to ride all over taking them away again. So why is this never mentioned?
While learning his new telepresence powers, Bran tries to talk to his dad in the past, and Ned calls out, "who's there?" I searched the first book and only Jon says "who's there" when Mormont is attacked by a zombie.
Soon Bran will be able to see anything anywhere, at least within range of a weirwood. It is less clear to me how he will be able to influence events. Animal attacks? Talking Ravens (Mormont's raven could be useful)? Or can Bran maybe make images appear in fires? Wooooo that would be interesting.