Duke of Milan
Although Prospero was an intelligent, honest and compassionate leader, he had two fatal flaws that caused his downfall: his inability to detect betrayal, and his passion for knowledge. Prospero mentions that he dedicated the bulk of his time to establishing his library and towards study, while leaving Milan's administrative responsibilities to his brother. Like Duncan in Macbeth, Prospero is unaware of the dangers surrounding him and is blinded by his emmersion in his books. Therefore, he has strong leadership abilities and intentions, but weak empthatic qualities.
Prospero as a father:
By today's standards, Prospero was a terrible father. He keeps his daughter ignorant about her past, treats her more as property than a human, and even casts her to sleep in order to keep her in the dark about his plot. However, I believe that for an Elizabethan audience, Prospero would have appeared as an ideal father (or perhaps it was Shakespeare's twisted ideal). He is protective, assertive, controlling, and understands her gender's weaknesses. All of his actions towards her are therefore justified because she is incapable of making her own decisions, and knowing what is best for her. In a sense, Prospero's parenting style only works because Miranda is one of the most plastic, stereotypical female roles ever conceived.
Prospero as a Magician
There is a strange dilemma here. Shakespeare needed Prospero to be a sympathetic protagonist, however, he was one that dabbled in magic which was highly frowned upon by the Elizabethan audience. Therefore all of Prospero's spells were immediately shown to be harmless. The best example of this is the scene immediately after the storm sinking the ship. Ariel makes it painfully clear to Prospero (and the audience) that no one was hurt in any way. This makes Prospero's use magic less 'sinister'. At the end of the play, Prospero relinquishes all of his powers before he journies back to Milan. This restores the natural order and shows that dabbling in magic should only be reserved for 'brave new worlds'.