In some ways, almost the entire story can be seen as an example of dramatic irony. This kind of irony is created when the reader or audience knows something that one or more characters do not. Montresor tells his audience immediately that he never threatened Fortunato but, rather, allowed the man to believe that he had no "cause to doubt [Montresor's] good will." Thus, we know a great deal more than Fortunato—that Montresor is actively plotting Fortunato's "immolation" for example—throughout almost the whole story.
When Montresor says that Fortunato is clearly busy and that he will go to see Luchesi instead, this creates dramatic irony because we know that Montresor has been searching for Fortunato specifically and will not seek out another local wine expert.
When Montresor explains that he had told his servants "not to stir from the house" and that he would not be home all night, he knows that this will "insure their immediate disappearance"; we know something that the servants don't, creating dramatic irony.
When Montresor says that the "gait of [his] friend was unsteady" due to alcohol, this creates dramatic irony because we know that he does not see Fortunato as a friend.
When Montresor offers Fortunato some Medoc as a "proper caution" against the cold and the nitre, we know that he is not actually concerned for Fortunato's health but is actually getting him drunk in order to manipulate him more easily.
In the end, however, one could argue that a different dramatic irony is created. Early on, Montresor said that one of his requirements for revenge is that he exact it with impunity, without incurring any negative consequences for himself. He now says that, when he went to fit the final brick into the wall that would imprison Fortunato, he "struggled with its weight." He has just erected an entire wall of these bricks, so it seems unlikely that he would just now struggle with one unless something else besides physical weakness were causing the struggle. Perhaps he feels guilty, making it hard to place the final brick.
After Montresor places the final brick, he says, "My heart grew sick—on account of the dampness." Again, though, the dampness hasn't bothered him this whole time, so why would it bother him now? Perhaps, again, his heart feels sick because his conscience is burdened by his deed. Further, the fact that he's telling this story some "half of a century" after the events could also indicate that he's been carrying around some guilt. If this is the case, then he has NOT achieved impunity—the burden of guilt is a negative consequence—and thus did not truly achieve his revenge, though he does not seem to realize this. Thus, dramatic irony is created here as well.