Adolin is definitely going to be showing a dark side in this book. I'm almost positive that Sadeas' death will have major consequences for Dalinar. If other people try to grasp for power, they could easily blame Sadeas death on Dalinar.
Because there is no evidence that Adolin is a Knights Radiant (that I'm aware of), I can almost assume that he may get envious of Shallan, Dalinar, and even Renarin. For once, he'll almost feel useless. All of the people around him are slowly becoming the heroes he'd always thought he was.
I'm almost positive that the guilt of possibly squandering Dalinar's reputation in this "new age" and his jealousy of people in the Knight's Radiant will lead him to do some erratic and unpredictable things. I'm honestly pumped and am excited to see how his relationship with Renarin, Shallan, and Dalinar change and evolve.