Evil is without question of major interest to Shakespeare in this play.  Without reviewing the political and social motivations for the evil characterization of Richard, clearly, Shakespeare is focused on exploring the varied aspects of an evil character.  Richard Gloucester seems a man without conscience, who can dissemble and plot, lie and manipulate so convincingly that the audience marvels at his audacity and daring.  We sympathize with his victims, because we realize that we too would be no match for his cleaver treachery.  What causes such behavior?  Shakespeare would have us believe that he is morally deformed, which corresponds to his physical deformity.  Modern psychology may more convincingly argue that reaction to his physical deformity has stunted his moral growth.  Richard says in his opening monologue, "And that so lamely and unfashionable/ That dogs bark at me as I halt by them--"  So one routinely ridiculed will likely come to see the world in a different light than a person who matures in a warm and nurturing environment.  But Shakespeare is less interested in motivation than in outcomes.

Because of the history involved, and because of the present monarch, Shakespeare emphasizes the closing of a bloody era of civil war and the healing effect of peace coming to England.  Richard is characterized as being the author of his own destruction.  He is disliked by nearly everyone including his mother, the  duchess. 

At the same time, Richard serves a larger purpose of purging the land of those elements which have fed the flames of war for nearly a half century.  In the final maelstrom of lying, stealing, cheating, and killing the country flushes from its system all the evil which can then be replaced by an era of  benevolence and understanding.  Well, that may be overstating the change that takes place.  Both Henrys and Elizabeth were fairly ruthless, but at least there were no more pitched battles fought between Englishmen on English soil for over 150 years.  And after what had taken place during the fifteenth century, most folk thought things were getting better.