A crucial component of the development of the free spirit is perspective - recognizing that there are many (or perhaps, unlimited) perspectives on all things, and then being able to see things from those other perspectives. The free spirit is striving toward "that mature freedom of the spirit which is fully as much self-mastery and discipline of the heart, and which permits paths to many opposing ways of thought." And he has to "learn that all estimations have a perspective, to learn the displacement, distortions, apparent teleology of horizons, and whatever else is part of perspective..."
In its most basic form, perspectivism develops as "theory of mind" in children, where they begin to understand that other people have separate minds and in particular, that their physical situation provides them with different perceptual inputs. Further development leads to grasping that other people have different emotional and even intellectual perspectives. While virtually everyone eventually grasps that these other perspectives exist, considerably fewer people develop the ability to apprehend the world from these other perspectives; fewer still can appreciate those perspectives and reserve judgment, and almost none can identify and address in this way a very wide range of perspectives.
Nietzsche seems clearly to hold that development toward these perspectival abilities is good, because of its link to justice: "power and justice and breadth of perspective grow upward together." claims there is a "necessary injustice in every For and Against," though this is likely not a pure relativism because "you had to see clearly wherever injustice is greatest."
Because this perspectivism applies to all things, in itself perspectivism is also only one perspective. There is at least one perspective that differs from perspectivism, viz., the meta-perspective that there is one universally privileged perspective (without specifying the particular perspective that is privileged). Thus there are injustices inherent in perspectivism itself - perhaps that it is painful to achieve: "Why so apart, so alone?"
If one were to take the approach of analytic philosophy in relation to this topic, the strong claim that perspectivism is privileged is manifestly contradictory when applied to itself. But Nietzsche is not an analytic philosopher, he makes no such claim, and he couches the entire program of the free spirit in a sweeping emotional flow that enables him to advocate and prefer perspective without contradiction.