The reliability of the narrator is a very common consideration when it comes to "A Tell-Tale Heart."
As one begins to read the story it soon becomes clear that there is a problem with the narrator. The eerie feel that pervades his account leaves the reader with the immediate impression that "something is wrong."
When a murderer tries to justify his actions there is every reason to be skeptical of his reasoning and his conclusions. The old man did nothing to bring his tragic fate on himself, it was all in the mind of the narrator. Who was the old man? Was this his father? Was it his grandfather? We are never told.
With the presence of the police his madness takes over to the point that he confesses on the grounds that they must hear the heart of the dead man beating under the floorboards.
There is little question that he is unreliable, except in his confession.