Successful execution: public order decreases via religious unrest (the people are angry at the presense of a heretic in their midst)
Unsuccessful inquisition: Public order bonus (Hooray! He's not a heretic!)
Presence in one of your territories: additional religious unrest, negative effect to population growth.
Finally, add some points to heresy targets, stuff that adds or decreases piety
Finally, have a chance at denouncing and executing the inquisitor! Targets of unusually high faith have an opportunity to reverse the tables on an Inquisitor without having to go through the services of an assassin. Add bonuses for things like association with the Royal Family, piety (obviously), chivalry and cruelty, etc.