The Tempest contains many moments of dramatic irony. For instance, many characters believe that others died in the storm, but the audience knows otherwise. Ferdinand and Alonso each believe the other has died in the tempest, and Alonso even threatens to drown himself in his grief. But the audience remains aware that everyone is alive and well despite dark thoughts and attempted murder plots, which deepen the drama without changing the fact that the play is, essentially, a comedy. This foreshadows the play's peaceful resolution; the audience gets the sense that conflicts will be resolved as they arise.
Another example of dramatic irony is the fact that Prospero rules the island. He seeks revenge on the royals who dethroned them. They, however, have no idea that Prospero caused the storm or is the island's ruler. This is dramatically ironic because the audience knows something that the characters do not. In Act 1, Scene 2, Prospero celebrates the fact that he will be able to enact his revenge:
By accident most strange, bountiful Fortune,
Now my dear lady, hath mine enemies
Brought to this shore; and by my prescience
I find my zenith doth depend upon
A most auspicious star, whose influence
If now I court not but omit, my fortunes
Will ever after droop.
Prospero has full knowledge of his enemies' presence, but they remain ignorant of him until later in the play. Here, dramatic irony serves to show Prospero's power; he is often portrayed as a playwright figure who controls the actions of the other characters and has more knowledge than anyone else.
Language is a prominent motif in The Tempest. In Act 1, Scene 2, Caliban curses Prospero for teaching him his language:
You taught me language; and my profit on't
Is, I know how to curse. The red plague rid you
For learning me your language!
He curses the man who taught him to speak because language allows him to understand his otherness. He feels trapped by the requirement to use the language of the captor who has deprived him of his freedom. He feels frustrated that this new power seems significant to Prospero but still leaves Caliban himself powerless in the ways that really matter.
Language also signifies the idea of civility—Caliban despises that he remains subordinate to Prospero despite having comparable linguistic capacity. Language is the single privilege Caliban has, and as he aptly observes, it does him very little good beyond allowing him to curse the rest of his circumstances. Shakespeare often makes the characters with high political status speak in beautiful verse, and the lower-status characters speak in simple prose, but Caliban shows great range in his capacity to put words together.
This is, then, an excellent example of situational irony because the very thing that many people assume would "civilize" Caliban ends up making him even more bitter and prone to cursing (which is the opposite of what most people would consider civilized behavior).