I think that there are two ways we can examine the character of the Duke in this poem. You can either view him as a very Machiavellilan figure who is able to use and abuse his power to manipulate others and send very clear messages about his power and supremacy, or you can argue that he is a figure who is so blinded by his arrogance and his position in the world that he is actually witless and is not aware of the possible ramifications of what he says and does.
Clearly, how we view the Duke revolves around our attitude towards what he says concerning his last wife and how she met her end. The way in which the Duke mentions her fate in an unspecific way could be viewed as either a very strong hint towards his companion about the kind of obedience and flattery he expects from his wife, or we could interpret it as a power-crazed comment from a Duke who is obsessed with his own importance and does not think of the consequences of his words. This, I think, is how the Duke could be viewed as being "witless," though my own reading of this poem leads me to the conclusion that he is much more cunning and Machiavellian than he ever could be considered witless.