How does Shakespeare portray Caliban in The Tempest and why does this portrayal sometimes contradict common public views of people like Caliban?
Once complicating factor is that because this is a play, the portrait of Caliban seen by an audience is very much a matter of the actor's treatment of the role. Also, how the audience will view Caliban depends on the cultural presuppositions of the audience.
Both in the Elizabethan era and now, a key factor in understanding Caliban is colonialism. For the Elizabethans, this would have meant the discovery of lands filled with brutal, bestial savages; Caliban's reaction of getting drunk and trying to rape a European woman reflects how Shakespeare and his contemporaries regarded indigenous peoples. A modern audience is likely to view Caliban more sympathetically, as we no longer consider indigenous peoples "savages" or "brutes" and respect Caliban's claim:
This island's mine, by Sycorax my mother,
Which thou tak'st from me....
...I am all the subjects that you have,
Which first was mine own king...