To understand Rorty's Philosophy and the Mirror of Nature, one must look at what he is not saying. He is not making an argument for why moral relativism is true. In fact, one could say that he isn't really arguing for anything, but rather, he is arguing against aspects of philosophy that seem misguided to him. For example, this book concerns truth, but it doesn't approach that discussion the typical way. Instead, Rorty describes the human faculty for "knowing truth" as a kind of honor system where we honor one another by agreeing with good-sounding ideas.
The main consequence of that argument is that Rorty ends up talking about truth not as an object to be held, but rather as a social device. The function of our sense for "truth" is essentially the process of jointly adjudicating different (inherently insufficient) points of view. In other words, what we call "truth" is just our participation in the language game of trying to sort through multiple points of view. That means that we're not even approximating objective truth, as other thinkers have argued.
This is different than typical postmodern moral relativism because it doesn't rely on the problem of interpretation the same way other philosophers do. This work is rather pragmatic in flavor, because Rorty chooses to look closely at what the practice of philosophy was originally designed to do. As a practice, philosophical inquiry exists for the communal good of the society, in Rorty's estimation. That also means that we mess with truth at our own peril.
