Well, he instilled a biased view on the public which persevered - I guess that is changing people's perspective. As a king, Richard III was never in danger of being forgotten though. His reputation was doubtless ruined in a moral sense by the Tudors, but history is written by the winners, right? In this case, by Shakespeare on behalf of the winners... Had he not had the play written about him, he'd be remembered in the general consciousness as a much better king, I expect.
Bottom line - Shakespeare isn't history, a lot of it was propaganda and reflected simply what was politic at the time.