I hope that Elhokar matures. Brandon likes playing with fantasy stereotypes, and one fantasy stereotype is the irredeemably spoiled young king. Dalinar cares enough about helping Elhokar grow up that it better happen. Dalinar is kind of the man.
I hope to learn more about Renarin (I believe that's his name--Dalinar's son). There's obviously some importance to him, what with his interactions with Wit and such. Definitely a character to come into his own.
I hope for the really tall Parshendi Shardbearer to become more of a force in the narrative, interacting more with Dalinar. Interesting, mysterious figure.
I hope that the story is set in another interesting city/location, a lot like how the Wheel of Time took the characters from one major city to another. They talked quite a bit about that one city naturally built around the windblade rock formations that rose in its center -- something's gonna happen there, soon.
Szeth the Surgebinder is off to go kill Dalinar, whose new head bodyguard is Kaladin...the Surgebinder. Mistborn Reloaded, anyone?
Obviously, Shallan's older brother isn't dead. Or if he isn't dead, he left a long, mysterious trail of clues/information.
Jasnah was quite defensive of King Taragavarariawhateverhisface. For being one of the smartest people in Roshar, you'd think she would know something about him. Is Jasnah evil, and involved with King Traraggvvaiean?
Also, some reveals as to the origins of the Shattered Plains, a closer look at the heart of the place, some reveals as to the gemhearts true purposes.
What are y'all's hopes/predictions?