In "The Tell-Tale Heart," the narrator is considered unreliable. The narrator insists that he is sane and intends to prove that he is sane, but his motivations and story call his mental state and credibility into question.
The narrator's unreliability relies on his attempts to confuse the reader, to digress and thus bury his omission of relevant information.
The real question is also if the Narrator who is also the first person can experience reality differently. To some extent, all first person narrators are unreliable. After all, they're recounting events filtered through their own unique set of experiences, beliefs and biases. There isn't just one absolute experience of reality.