Most Poe narrators are unreliable first person narrators. This doesn't necessarily mean they don't show up when they say they will, but rather that they either can't or won't tell us what really happened.
In this case, the narrator is trying to prove his sanity. One bit of proof he offers is his ability to exercise "dissimulation" (to act or speak one way to mask true feelings or intention) with the old man. So, if he's trying to prove he's sane, and dissimulation is a proof of sanity, doesn't that suggest his probably using the old dissimulation on us, too?
The narrator also admits that due to his intensely powerful sense of hearing, "he can hear all things in the heaven and in the earth [and] many things in hell" (1). So, he isn't gripping reality very tightly, due in part to a sick mind, and in another part to a sick body.
On occasion, he also pretends to be an omniscient narrator. He tells us how the old man feels and what the old man is thinking. Here's an example: "Presently I heard a slight groan, and I knew it was the groan of mortal terror. […] I knew the sound well. Many a night […] it has welled up from my own bosom" (5).
As you can see, the narrator's insight into the man's head is just a reflection of his own experience. Yet, he's probably right. In this moment he humanizes both himself and the man through empathy.
Unreliable narrators are compelling because they represent a basic aspect of being human. We all experience moments of unreliability, where we can't perceive or remember events accurately. We all get confused and do and say things we don't mean or don't mean to do or say. In a story like "The Tell-Tale Heart," this unreliability is taken to extremes.
The scare power in this technique is the nagging knowledge that we could become a person like the narrator, or a victim of a person like the narrator, a person whose inner unreliable narrator has totally taken over.