Character Analysis
The Duke is one bad dude. He's apparently poisoned a number of young women who refused his sexual advances (2.3.146), and he's more interested in his reputation than in justice, as the trial scene with Junior indicates (Act 1, Scene 2). He's slippery, first insisting that justice be done after his stepson Junior rapes a woman, and then backing off and deciding the case should be heard later.
He's also pretty hypocritical. Given that the Duke has been poisoning young women who won't sleep with him, his first insistence on justice here sounds a trifle insincere. In any case, he doesn't manage to stand by it, so he's also rather unreliable.
The Duke is fairly clever, though. He manages to see through the scheming of his stepsons (Act 2, Scene 3) and he thwarts them pretty effectively. You can't be this bad for this long without learning something, we suppose.
The Duke also shows a bit of self-awareness in his scene with his stepsons (2.3.141-149). Is he genuinely feeling some guilt over his wrongdoing? Or is he just engaging in another specious argument? A lot depends on the actor playing the part—but either way, he won't escape V for Vindice.
Duke's Timeline