The Duke, especially, announces that he is doing one thing, and then acts completely different from his stated intent. This calls forth questions why the Duke would be deliberately misleading, and what his overall intent for this deception of leaving the city is.
Appearance vs. reality
Applies to Angelo especially, whose reputation and appearance of goodness do not match the reality of who he truly is. Also applies to city of Vienna, which appears pretty and peaceful, but hides a lot of sin.
The city in this play is corrupt, just as Angelo becomes so. This corruption seems to be the result of too much indulgence, or a belief that one will get away with one's crimes.
Vice vs. Piety
Several figures in the play seem to err either toward being too indulgent or too strict; the play attempts to punish those who are too licentious, and teach those who are too pious, by the time the end is reached.
Whether a person can resist temptation is a sign of how good or wicked they actually are. Temptation plays on the tendency of human nature to be flawed and vulnerable, and those who allow themselves to be tempted too far are weak of character.
Allows all of the Duke's machinations to take place. Without disguise, and the way the Duke uses and abuses the privileges that this disguise affords him, many events in the play would not have taken place at all.
Moderation and mercy
These are the two necessary qualities of a ruler that Angelo lacks, and which make him a poor judge. Every ruler must govern with an eye for human nature and its weaknesses, and show mercy for those who commit the same sins as the ruler himself falls victim to.
Key to the plot, as most of the events in the play are manipulated by the Duke. Without his manipulation of people and events, Claudio would have died, Angelo have remained unexposed, and Mariana would not have gotten married. Justice depends upon the Duke's machinations and manipulations within the play, however self-serving his actions may turn out to be.
Measure for Measure Questions and Answers
The Question and Answer section for Measure for Measure is a great
resource to ask questions, find answers, and discuss the novel.