Is the Duke a benign (but lazy) Magnificent Bastard, or is he just doing it for the lulz? Consider that he poses as a friar and consoles men condemned to death (whom he plans to ultimately pardon, of course). In the time the play was written, the eternal damnation of the soul and the right of priests, and priests alone, to grant absolution were taken very, very seriously. In modern terms, the Duke's deception would be like some unqualified meddler pretending to be a surgeon and performing life-or-death surgery.
Unless, considering this play was written and performed in Protestant England, the faith that Catholics put in priests and friars is meant to be a big joke, and the audience should laugh along with the Duke as he merrily dupes one schmuck after another.
Heartwarming Moments: Mariana is pleading for her new husband Angelo's life, and asks Isabella to get on her knees before the Duke to help her. Angelo tried to rape Isabella, broke his promise to spare her brother in exchange for sex, and has been Isabella's enemy for the whole play. Increasingly hysterical, Mariana begs Isabella to get on her knees, and none of the bystanders think she will...And then Isabella gets on her knees beside Mariana and begs for Angelo's life despite all he tried to do. A beautiful example of the Christian mercy that as a future nun (maybe), Isabella should be practicing.
What makes this doubly heartwarming is that she now shows genuine mercy, not the cold, distant mercy she showed her brother earlier.
Strangled by the Red String: Some see the Duke's proposal to Isabella as this, seeing as how their interactions up to that point have no romantic chemistry whatsoever, and it almost seems like Shakespeare addressing the awkwardness of a Pair the Spares happy ending.
True Art Is Angsty: This is one of the darkest of Shakespeare's comedies. But it's also one of his less popular plays. Perhaps that fact averts the trope, ultimately.