These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Or Prospero and Miranda. A psychoanalytical (Freudian) reading would tell us that Prospero, Ariel and Caliban are in fact the same person and Prospero follows his inner desire (id, that is, Caliban) and goes to rape Miranda, stopping himself at the last moment. There's loads of "proof" of this throughout the play but as any English teacher will tell you there's loads of proof for whatever reading you choose, so ... your mileage may vary.
Ditto with Miranda and Caliban. Some versions imply that Caliban didn't rape Miranda, but just got caught having a torrid affair with her.
Caliban- nasty brute or Noble Savage? His appearance has been much debated with interpretations ranging from some kind of ape man to a fish person, to a normal, non-white human.
Prior to the events shown in the play, was Prospero a wise ruler who studied magic on the side, or was he just a deluded old man who cared more about magic than about his family and responsibilities? Is his antisocial personality the result of his righteous anger at everyone who wronged him, a byproduct of his years of isolation on the island, or has he been that way ever since he took up magic?
Antonio. Is he a self-serving bastard who only cares about power, or is he a pragmatic politician who understands the business of ruling far more than his Absent-Minded Professor brother?
Ensemble Darkhorse: Caliban has grown in popularity and sympathy with scholars over the centuries.
Epileptic Trees: There are as many interpretations of the play as there are critics. Who and what Caliban represents takes up half the debates.
Values Dissonance: In modern times, the play seems like an early example of fantasy fiction and stands in contrast to Shakespeare's famously realistic settings. As a matter of fact, in the Elizabethan era, it was hardly an issue for audiences to suspend their disbelief in order to accept a wizard as a protagonist because many people did indeed believe in magic.
The character of Caliban, who has been interpreted more sympathetically in Postcolonial analyses than he was in Shakespeare's day.
Viewer Gender Confusion: Ariel. In the text, he's male, but he's also a fairy, and most modern English speakers think Ariel sounds like a girl's name. He is most likely supposed to be androgynous, and is as often played female as male.