I studied this poem last year and i really loved it.I guess  the use of dramatic monolgue(in which Browning impersonates a character of a duke) is the focus of attention as Browning introduced it as a new technique and paved the way for the poets who followed in his steps by introducing experimental techniques.

To know the meaning of "dramatic monologue" check this : http://www.english.uga.edu/~232/voc/dramatic.monologue.voc.html

Another point is that the poem depicts the victorian notion :Wealth and power replace truth and values.In this poem we no longer speak of truth and values(love,nature as a medium to reach the Sublime etc...) but rather of power(the duke, his title,his control over his wives,etc..) and wealth.

Finally, the title itself is ironic. I mean the word "Last" means that there were duchesses before her and there will be after her.

Hope i was helpful,

Best wishes.