The Duke's Substitute
The governing irony of the play is that the Duke, who admits to being a somewhat ineffective ruler, temporarily replaces himself with the corrupt and malicious Angelo. Thus, the play vacillates between two governing extremes: complete laissez-faire policies, which lead to moral decline, and over-the-top austerity, which breeds fear and anxiety among citizens. One might argue that the play attempts to address the age-old question of whether a ruler should be loved or feared by their people.
The Friar
When the Duke disguises himself as the friar, it serves as an ongoing dramatic irony throughout the play. Nobody – especially Angelo – has any idea that the allegedly departed Duke is among them, watching the new governance of Vienna that he himself implemented. The play pokes fun at the Duke's behavior, suggesting that his disguise was completely unnecessary and inappropriate given his political role.
Claudio's Death
At the end of the play, Isabella has no idea that her brother was not actually executed. The Duke, in disguise, allows her to believe that Claudio is dead until the final moments of the play despite what the audience already knows.
Angelo's Proposition
Angelo sentences Claudio to death for fornication after it is discovered that Claudio and Juliet, though betrothed, have engaged in premarital sex. Later in the play, Angelo propositions Isabella for sex under the guise that if she accepts, he will free her brother. The irony of his proposition is that he will happily participate in the same illegal activity (fornication) for which he has warranted Claudio's execution, underscoring his hypocrisy as a corrupt leader.
