The question -- what is some evidence from Edgar Allan Poe's short story The Cask of Amontillado that proves the narrator is unreliable -- is interesting insofar as there is nothing that suggests that the narration is unreliable, but much to suggest that the narrator, Montresor, is intrinsically duplicitous in his dealings with Fortunato. This is an important distinction. To suggest that Montresor is an unreliable narrator, one would need evidence of some sort that the story he relates is untrue, or fundamentally misleading with respect to the chain of events described. There is no indication, however, that Poe intended the reader to question the validity of his narrator's tale. On the contrary, Montresor is depicted as the quintessential homicidal sociopath, driven to this state, as he indicates in the story's introduction, by the "thousand" insults he has endured at the hands of Fortunato. Montresor's story, we must presume, is accurate. He has killed Fortunato, and by the means described. He is, however, duplicitous in his dealings with his intended victim, evident in the following passage:
"I gave Fortunato no cause to doubt me. I continued to smile in his face, and he did not understand that I was now smiling at the thought of what I planned for him, at the thought of my revenge. . .I acted pleased to see him, and I shook his hand, as if he had been my closest friend."
As the above passage indicates, Montresor is betraying Fortunato's trust as the key to achieving his objective of avenging the latter's repeated if unspecified insults. Indeed, Montresor is duplicitous by nature, anticipating the worst even in his own household staff, as when he describes the manner by which he ensured that that staff would be away when he brought Fortunato to his home:
"I had told the servants that they must not leave the palace, as I would not return until the following morning and they must care for the place. This, I knew, was enough to make it certain that they would all leave as soon as my back was turned."
Montresor is not unreliable as a narrator; he is unreliable as a friend, and there is a difference. The reader must presume that the narration is accurate, as the murderer is confessing his sin without remorse, and in a manner that leaves one to accept the tale as told.