Remember that during the Renaissance both the general public and the paid artists were undergoing a major change in thought. Gone were the days were people acted in ways that assured them of a place in heaven; these people did things that made them happy in their worldly life. How could they not with kings like Henry VIII in charge?
Because of this change in thought, Shakespeare's characters are often attempting to obtain the unobtainable. Romeo and Juliet are after the perfect love; Julius Caesar and Macbeth chase the perfect rule; Petruchio wants the perfect wife; etc. etc.
Shakespeare's pal Christopher Marlowe, who was unashamed to self promote whenever possible, would have been the first to tell you that writers and artists needed "feel-good" stories to entertain the people or else they would be out of work.
Tons of ways! His characters show their innovative thinking, their flare for art and music, issues with religion and other current events. Class structure was huge in all of Shakespeare's plays as well. Shakespeare was like today's Stephen King...whatever thrilled the masses or stirred their emotions in some way...made it into Shakespeare's plays.