"Rough" and "un-poetic" are good terms to apply to "My Last Duchess." Robert Browning's dramatic monologues are intended to characterize the speaker as well as to present a dramatic narrative. In this dramatic monologue the meter is a rather graceless and intermittent iambic pentameter, and the lines are simplistic and frequently awkward rhymed open couplets. The effect is to characterize the speaker as a coarse and vulgar man in spite of his pretensions to be an art lover. He himself admits that he lacks skill in expressing himself.
Who'd stoop to blame
This sort of trifling? Even had you skill
In speech — (which I have not) — to make your will
Quite clear to such an one, and say, "Just this
Or that in you disgusts me; here you miss,
Or there exceed the mark"
The couplets are the most glaring signs of the Duke's ignorance, insensitivity and stupidity. Here are some examples of ending rhymes:
Art does not have to be beautiful. The function of art is to communicate feelings, and a work of art can communicate unpleasant feelings as well as pleasant ones. Pablo Picasso proved this with many of his paintings. "My Last Duchess" communicates the same feeling about the egomaniacal Duke that is obviously experienced by his visitor, who can't stand any more and hurries down the stairs without a word of apology or explanation in order to advise the Count to find any excuse to break off his daughter's engagement to this aristocratic monster, who has had his "last duchess" murdered because she was too happy and smiled too much.
Robert Browning's language in "My Last Duchess" is intentionally "rough" and "un-poetic" because it characterizes the speaker as vulgar and insensitive in spite of his "nine-hundred-years-old name." Instead of appreciating the poem for its gracefulness and subtlety, as we would with one of Shakespeare's sonnets, we appreciate "My Last Duchess" for the craftsmanship that went into creating its many bad features. We are not told what the speaker looks like, but we cannot help visualizing him as an exceptionally ill-favored man dressed in elegant clothing.