The Poet's Laurel (Verbal Irony)
Although we cannot say for certain, some have speculated that Dante is ironically praising himself throughout the Paradiso, especially in the places where he refers to the poet's "laurel crown" (XXV.9). This irony, if present, would likely be due to Dante's knowledge that his outspoken politics and idiomatic theology might prevent him from the sort of political and institutional support that a poet like Virgil once received.
Dante's Sight (Situational Irony)
Twice in the Paradiso, Dante loses his sight. Yet these moments often come exactly at the moment that his sight is about to be literally and metaphorically strengthened. Thus, these moments of loss become, ironically, moments of great benefit for Dante.
The Poet's Defeat (Verbal Irony)
On a number of occasions, Dante clearly announces that he has reached his limit as a poet, whether in his ability to describe Beatrice or to recount an event in heaven. And though this may be a strange form of irony, it is still somewhat ironic that Dante announces this limit and then immediately proceeding to attempt to describe what he is seeing; it is as if he is acknowledging his failure but subtly nudging the reader to enjoy watching him transcend it.
Phaeton's Flight (Dramatic Irony)
Throughout the Paradiso, Dante makes frequent references to Phaeton, a mythological figure who, irresponsibly flying the chariot of the sun, was struck out of the heavens by Zeus's thunderbolt and killed. In these allusions, he often compares himself to Phaeton, creating a sense of dramatic irony for the reader, who might wonder if Dante is unaware that he himself could be struck by lightning and killed. Of course, Dante is "struck by a bolt/of lightning" in the final canto, but this is a beneficial, rather than a harmful, bolt. Dante thus creates tension through dramatic irony, but he diffuses this tension by changing aspects of Phaeton's story.