It is told in the 3rd person, with a limited narrator. It is the duke himself speaking, and that is the only perspective we get. It is just a monologue of his thoughts and perspectives. So, his guest's thoughts are never portrayed, and we have to infer what the guest is thinking based on what the duke says. For example, at the end, we can guess that the guest was attempting to leave when the duke states, "Nay, we'll go together down, sir,". He wants his guest to wait, to not be so anxious to leave. Because of this limited perspective, it gives us a really great glimpse into the psyche of the duke, but very little into the actual reality or facts of what he is speaking about. We don't know for sure if his first wife was too flirtatious or unfaithful as the duke implies, because it is just his perceptions.
There is no evidence to suggest that the poem is about Robert Browning's first wife; rather, it is speaking of the narrator's first wife,the man that Browning creates to tell the story. Browning had a knack for creating creepy characters who go to great lengths to secure love, and the duke is a great example of that.
Browning’s inspiration for "My Last Duchess" was the history of a renaissance duke, Alfonso II of Ferrara, whose young wife Lucrezia died in suspicious circumstances in 1561. Lucrezia was a medici– part of a family that was becoming one of the most powerful and wealthy in Europe at the time. During Lucrezia’s lifetime, however, the Medici were just beginning to build their power base and were still considered upstarts by the other nobility. Lucrezia herself never got to enjoy riches and status; she was married at 14 and dead by 17. After her death, Alfonso courted (and eventually married) the niece of the Count of Tyrol.