One of Prospero's major strengths is that he can do magic. We don't know precisely why—not all humans do magic, obviously, even those on a magical island—and he seems to be able to do so immediately, even before the book and staff. (Look at when he frees Ariel from the cloven pine, for example.) I would call his love for his daughter a strength. As for weaknesses, well, those will vary by period. I see his drive for power and revenge as a weakness, and his suspicion of other people, but I'm not sure Shakespeare's period would have. He seems brusque with Ariel at times, as in this line, when he threatens Ariel: "I will rend an oak / And peg thee in his knotty entrails till / Thou hast howl'd away twelve winters"