Poe writes, "Slowly, little by little, I lifted the cloth, until a small, small light escaped from under it to fall upon—to fall upon that vulture eye!" By repeating "to fall upon" with an em dash, Poe slowly lifts the veil on the horrors of that night; he takes his reader to the very moments the narrator relives.

In the final paragraph, Poe's narrator illustrates his fervor with eight exclamation marks. He has committed an act of horror, and he can no longer refrain from shouting it!

I'll pick words and phrases that are repeated throughout "The Tell-Tale Heart."  The narrator, very early on in the story, tries to establish his sanity.  In fact, the narrator reminds the reader throughout the story that he is not crazy.  The words "mad" and "madness" are used a total of seven times throughout the text.  For example, from the opening paragraph:

I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad?

How is he not crazy?  The man just admitted to being able to hear stuff from heaven and hell.  That sounds crazy to me.  He continues to attempt to prove his sanity by telling the reader that he couldn't be consumed with madness, because he was really careful about stalking and killing the other guy.  

Now this is the point. You fancy me mad. Madmen know nothing. But you should have seen me. You should have seen how wisely I proceeded—with what caution—with what foresight—with what dissimulation I went to work!

I have news for the narrator.  Just because a person is careful and exercises caution, doesn't mean he is, or is not, crazy.  I'm sure certified serial killers in real life also think they are not crazy.  

Poe uses punctuation to good effect in the opening passage of “The Tell-Tale Heart.” Here, we are confronted with an unreliable narrator, a young man desperate to convince us that he isn't really mad. And yet the punctuation used seems to contradict what he's saying.

First and foremost, there are quite a lot of dashes in the opening paragraph. This would appear to indicate that the narrator's thoughts are moving quickly, unable to settle for any appreciable length of time. The narrator tells us he's nervous, and that nervousness is more than adequately conveyed by the profusion of dashes in the story's opening.

But the dashes hint at something more, something that the narrator flatly denies: his madness. The narrator is at great pains to convince us that he isn't mad, but all those dashes, chopping up his thoughts into little pieces, would suggest otherwise:

The disease had sharpened my senses—not destroyed—not dulled them.

Madness can often have the effect of heightening the senses, and so we're not particularly convinced by the narrator's protestations of sanity.

Furthermore, the short, snappy sentences in the opening paragraph only serve to heighten our suspicions that the narrator is not all there, especially when he says things like this:

I heard all things in the heaven and in the earth.

Although the narrator is keen to convince us that he's sane, what he says and the way in which he says it indicates that he's not just nervous but mad.

To be clear, Poe is not the narrator of this story. The narrator is some young(ish) man who lives with an older man, perhaps his own father, and who has grown obsessed with the older man's "vulture" eye. Poe uses lots of exclamation points throughout the work in order to characterize the narrator as highly volatile and excitable: as someone who does not seem to be quite in control of himself or his feelings or fears.

In the first paragraph, for instance, such an exclamation point occurs after the very first word, "True!", making it seem as though we, the audience, are being shouted at from the start. The narrator goes on to state that his senses are sharper than typical and that he can hear everything that takes place in heaven and on the earth—even some things in hell. "Hearken!" he tells us, and he invites us to hear how calmly he can tell us the story.

In the third paragraph, likewise, the narrator continues to exclaim. He says that he was so good at deceiving the old man and brags about "with what dissimulation [he] went to work!" He explains how he would open the old man's door every night "oh so gently!" He even insists on his thoughtful wisdom, saying, "Ha! would a madman have been so wise as this."

All of these exclamation points, and there are a great many more throughout the rest of the story, show (rather than tell, since the narrator is the main character himself and he thinks he is tranquil) how excitable he is. He insists over and over that he is perfectly calm, but the repeated use of this kind of punctuation lets us know that he is actually volatile and unstable and—though he denies it—quite mad.