Frustration and disenfranchisement
This story takes its title from a central character, Prospero, and the movie also portrays him as the central point of view, because Prospero narrates the story. Prospero's story is specifically oriented around his struggle to reconcile the hatred and betrayal he feels from years of disenfranchisement. He curses the cast of this story to come to the island and work through their beef with him, and old fights resurface between the Italian factions. Before this story, Prospero was prosperous, a duke in Milan of all things. That detail helps show how much he lost when his community exiled him for being different.
Chaos and primal instinct
Although Prospero has lost many of his European niceties, he has replaced them with something more instinctual. He regularly consults with an island fury, Ariel, and one could easily argue that in a way, Caliban's character exists to illustrate a part of Prospero's personal psychology. In a word, Caliban is like a child, except he is deformed and handicapped, illustrating that Prospero feels monstrous and animalistic because his social community resented him for his chaotic elements.
Identity and secrecy
Guess what shouldn't be happening on an island after a crash-landing: a masquerade. Nonetheless, it happens and it's a central focal point in the plot. The imagery of the masquerade shows what this tempest summoning wizard resents about his Italian cohorts. It is that they withhold their true intentions under a mask. Although most people could easily realize they are simply being polite and naïve, Prospero battles paranoia, because he just wants people to understand who he really is, and that isn't the game they're playing whatsoever.
