I heard he has more to say than your other party members when you visit the Dalish Elves for their help against the Blight. That aside, he has a personal random encounter in Denerim that can go many different ways depending on his approval rating. --- A clever little bleeder, was Oscar Wilde. He once defined a cynic as a man who knows the price of everything and the value of nothing. Call me a cynic, then.
He will ask you about your plans to be queen or king, after the Landsmeet, if you are a Human Noble. Ask about Antiva (to get the Boots quest). Ask about the Dalish (to get the Gloves quest, which is only available after entering the Dalish camp and talking to Mithra).
I believe the "quest" is just a random encounter in which you meet another crow and zevran decides to betray you or not. After that point, his meter changes from "warm" to "friendly" (what happens after other companion quests).