I would certainly want to know exactly why he is so angry with Fortunato. I would ask what these "thousand injuries" are that he mentions in the first sentence of the story. Montresor says it is an insult that sends him over the edge. He is so offended by this insult that he vows his revenge. What is the insult? How could an insult be so bad as to make a man want to bury another man alive? Montresor comes across as a cold, calculating, vengeful man. I might ask him if he is mentally stable. Given his dubious state of mind, I might ask if he is proud of how he tricked Fortunato and lured him to his own death. In the opening paragraph, he says that his plan for revenge is definitive and that "the very definitiveness with which it was resolved precluded the idea of risk." In other words, he is so determined and so sure of his plan that he feels there will be no risk. So, I would want to know if he is proud of this "perfect" plan. Or, I would ask if he would have attempted the murder if there would have been some risk, some possibility that Fortunato would figure him out or that Montresor would become a suspect in the case of Fortunato's disappearance.
I would ask if he has even a hint of guilt or remorse for what he has done. Or, if I were a police detective, I might ask if this is something he's done before. Does he have a history of violent thoughts and behavior or was this an anomaly in his life?