This is a huge question. I'll point you toward the main characters and events in the play that concern morality and corruption, to give you a general starting point. The contrast between choosing to act in a moral or corrupt fashion is a major theme in this play, and as Shakespeare often does, here he provides no easy answers to this question. Rather, he creates characters who passionately believe in this or that action as moral or corrupt, and the ensuing interaction between these characters (with the opposing points of view) creates conflict, which creates drama.
The main plot of the story revolves around the triangle of Isabella, her brother Claudio and the man who holds the power in Vienna while the Duke is absent, Angelo.
Angelo, rules with an excess of morality. As soon as he gets his hands on the power, he shuts down brothels and makes it his mission to see all moral corruption punished and eradicated from Vienna. As part of this new regime of "morality," Claudio is arrested and sentenced to death for impregnating his fiancee. In essence, Claudio is to be killed for having sex with a woman out of wedlock. Angelo, in the opening of the play, appears (on the surface) to have extremely high morals. But, later, when he attempts to coerce Isabella to make a deal with him (He will save her brother from death if she will sleep with him.), he is revealed as much more corrupt that his initial actions suggested.
Isabella is a novice, in training to become a nun. When her brother asks her to beg for his life to Angelo, she visits Angelo, only to be offered the corrupt "deal" from him to save her brother's life. When she visits Claudio in jail to tell him that she cannot act in an immoral way, even to save his life, he is heartbroken. Yet, Isabella stands firm, refusing to compromise her morals.
Claudio might well be the most human (which is to say, the most morally ambiguous) character in the play. At first, though he is bitter that the law under which he has been arrested hasn't been enforced for many years, he seems ready to prepare himself for death. Once his sister apprises him of Angelo's "deal," however, he seems more than willing to push his sister completely against her own moral conscience for the sake of saving his life. Claudio's weakness and readiness to adjust his sense of morality to fit his own needs and desires, may be the best example of how the common man might react given this situation. Claudio represents the flawed and ultimately selfish nature under which most humans operate.
This idea of "selfishness," and how it influences the choice to behave in a moral or corrupt way, is certainly a factor for all three characters. Claudio, selfishly, desires Isabella to compromise her morals to save his life; Isabella selfishly (to preserve her chastity) refuses; and Angelo selfishly throws his own moral standards out the window to, potentially, gain pleasure with Isabella.
For more on these characters, please follow the links below.