How reliable or unreliable do you consider the narrator? And why?
Montresor appears to have written a letter to a close friend whom he addresses as "You, who so well know the nature of my soul." In other words, he is not addressing a general audience. The story seems to be a letter found among some papers after the death of the recipient and translated into English by an editor named Edgar Allan Poe. Or it might be a letter written by Montresor one night when he was drunk and never posted because he thought better of it next morning. So there is no reason to think Montresor, the narrator, might be intentionally deceiving "You, who so well know the nature of my soul." It is possible, however, that he could be deceiving himself a little--but just a little. There is one point at which he seems to be denying that he has any feelings of guilt or pity for the terrible murder he is committing.
My heart grew sick; it was the dampness of the catacombs that made it so.
This we do not believe. We think his heart grew sick because he had accomplished the perfect murder he had been envisioning for so long, and now he realized he was doing an unpardonable thing. He might have thought about how he would have to be punished for this sin in the afterlife.He might have thought about how he would have to keep this secret to himself for the rest of his life. He might have thought about how he would have to pretend to be just as concerned about Fortunato's disappearance as everybody else. But he suppresses such feelings and thoughts and deceives himself by attributing his sick heart to the dampness of the catacombs.
Otherwise, it is not easy to detect any clues that show Montresor is an unreliable narrator. He is certainly unreliable in everything he tells his victim Fortunato, but he is not telling the story to his victim. As a matter of fact, he never makes the slightest attempt to tell Fortunato why he is doing what he is doing to him. Fortunato should have plenty of time to speculate about that before he dies of madness and starvation.