Prospero's manipulation of nature by his art (natural magic in contrast to Faustus's necromancy). Francis Bacon, a contemporary of Shakespeare's and one of the originators of empirical and experimental scientific methods, thought that if people understood the workings of natural forces, they might be able to control storms or carry out other tasks that we see Prospero doing in this play.
But Prospero's powers are always potentially double-edged--his "dark twin" is the witch Sycorax whose history is oddly parallel with his own. Will Prospero resist the temptation to use Sycorax's cruelties against his enemies?
The limits of the art of illusion: see 4.1.146ff, the emphasis on insubstantiality of human life and art.
Another limit addressed by the play: what are the proper limits of revenge?
The importance of "sea change" in the play, its interest in metamorphosis. Prospero's undergoes transformation: he re-enters society as a secular prince, the master of a state, not the master of magical arts.
The limits of transformation/conversion: no words of repentance from Antonio; Prospero's own very grudging forgiveness of Antonio.
The representatives of Europe, of theOld World, constitute the New World to Miranda. The play insists upon the complexity of human experience (we're offered a new spin on the double vision of the New World it has already offered.).
The double voice of Prospero/the actor soliciting our applause: Only the audience can free Prospero from his island, send him home, complete the action of The Tempest.
Prospero places himself in the Caliban position: he must beg not to be confined "in this bare island." And don't neglect the Christian resonance of the final lines: Prospero prays for the audience's grace. If Prospero is now (again, like Caliban) "seeking for grace," we have been promoted to the role of God.
Does the artist's need for the reader's/audience's grace ultimately put a limit on the artist's self-deification? Prospero can only escape his island by embracing the imperfect, fallen magic of human community.