One view is that Montresor is an unreliable narrator because of his deranged attitude and behavior toward Fortunato. Another view might be taken wherein Montresor's behavior toward Fortunato is separated from the narrative he reports about his behaviors and about events leading up to Fortunato's entombment. With this separation of behavior from narrative of behavior, it might be argued that, although Montresor is maladapted in his social expectations, responses and actions, he is a clear and reliable reporter, or narrator, of those expectations, responses and actions.
By this argument, we accept that Montresor's report of offenses against him by Fortunato is accurate, although filtered through a maladapted social lens. For example, Fortunato, a Freemason, might not have given enough respect and deference to Montresor's ancient and noble ancestral origins and accomplishments; Fortunato may have been a modern man who gave respect to merit above ancestry. To Montresor, this may equal to a "thousand injuries."
Further, by this argument, we accept that Montresor performed the chilling deed just as he reports having performed it. We have to wonder, then, to whom he is narrating his chilling tale "the half of a century" after he "re-erected the old rampart of bones" against Fortunato's unfortunate tomb.
Some suggest he is telling his narrative to a psychiatrist or a police official. It may also be suggested that he is telling his tale to an heir, a family member to whom the character of fortune's benefactor is being precisely, even vainly drawn: an heir to whom Montresor is baring his soul while expecting it to be admired (for upholding the family honor).
So, by this argument--the argument that Montresor is socially maladapted but perceptually acute and accurate--it may be said that Montresor is a reliable narrator giving an incomprehensible reality to a horrific tale of "vowed revenge" and "punishment with impunity."
I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat. At length I would be avenged; ... the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.