"The Cask of Amontillado" is written in the first person. This point of view is particularly effective because it enables the author to delve into the emotions and motives of the protagonist Montresor. The whole purpose of the story is to show how his perfect revenge gave him the satisfaction he desired. This point of view is also particularly effective because the reader is entirely dependent on the narrator for information, which could be true or false.
One detail in the story that makes the narrator seem unreliable is his failure to explain any of the "thousand injuries" he has suffered from Fortunato. Many readers have suggested that Montresor might be insane and that all the so-called injuries were imaginary. If Montresor is indeed insane, then his whole story might be considered unreliable. Apparently the cask of Amontillado does not really exist. Montresor is certainly unreliable from Fortunato's point of view. Montresor keeps calling him "my friend" and showing the greatest concern about his health, when the truth is that he hates him so much that he intends to kills him in the most horrible fashion.
If Fortunato is the only other character in the story, and if everything Montresor tells him is a falsehood, then it is clear that the narrator must be considered unreliable. The reader is getting much of the same information from the narrator that Fortunato is getting. Most readers probably believe that the cask of Amontillado actually exists and that the two men will eventually get to it as they wind their way through the gloomy catacombs filled with wine barrels and human bones. At what point does the reader suspect that there is no cask of Amontillado?
The story appears to be a translation of an old letter which somehow came into the hands of the author, Edgar Allan Poe. Montresor is addressing someone whom he trusts because they have known each other for years. There is reason to be skeptical about someone like Montresor having such a good friend or of trusting anybody. This letter might be full of inaccuracies or deliberate falsehoods. It does not necessarily have to have actually been sent to the friend. It might have been written but never mailed, only kept in a strongbox or secret place and discovered after Montresor's death.
Montresor's narrative could be a complete fiction--and in fact it is a complete fiction, because the whole story was iinvented by Edgar Allan Poe. The cask of Amontillado sherry itself is a double-fiction, because it was invented by Montresor, a character who was invented by Poe.