1) R' Gil Student, who started the effort to define it, plays the disingenuous card, claiming that it's just a sociological observation, Post Orthodox does not necessarily imply Non Orthodox, but here are a number of ideas which, if you hold a lot of them, would make you Post-Orthodox. Note that a lot of the ideas are themselves non-Orthodox, while others are themselves are perfectly normal ideas in Talmudic study (see my previous post); what unites them is Gil's unstated-but-real attempt to define a class of people who are no longer Orthodox because of the collection of ideas they hold. That is, it's an attempt to disenfranchise part of the left wing of modern Orthodoxy.
2) R' Jeffrey Woolf has been inching towards trying to define Post-Orthodox as a theological narrowness of vision, turning Judaism into soulless practices that may be solidly based on texts, but do not reflect the weight of Jewish tradition or a concern with using one's ritual observance as a tool with which to build a relationship with God. He thus applies it equally to Right and Left.
The Left creates practices that were never seen before, or at least not in recorded history, that are based in classic texts, that may feed the zeitgeist, but little thought is given to how they will increase people's attachment to Hashem and to traditional practice.
The Right, with its concentration on humra, also increases the punctilio of observance, but in so doing, they don't really pay attention to the classical vision of humra as a personal practice that increases one's attachment to Hashem and His Torah; and by drawing their theological boundaries ever narrower, their new text-based humra culture excludes many Rishonim and Acharonim from the pale of Orthodox belief.
3) R' Brill, who initially posted on Post-Evangelicalism, and speculated on whether there might be a Post-Orthodoxy parallel to it, strongly rejects Gil's idea that it should be the basis for creating a schism, and driving the out fringe of LWMO out of Orthodoxy. Not that he says so directly, of course. Rather, he defines Post-Orthodox narrowly, as a parallel to Post-Evangelicals, of people who self-defined as Orthodox, many of whom were in fact raised Orthodox, but chose it in adulthood as well, mostly in the 1970s through early 1980s, and then regretted their decision. So they left Orthodoxy, consciously, for whatever personal reasons, but continued to struggle with finding a religious identity.
R' Brill's primary example is Rebecca Goldstein, PhD, who wrote an autobiographical novel and a book about Spinoza. She chose Orthodoxy, lived in Orthodox towns (Teaneck and Highland Park), and then left. Her writing seethes with her continuing obsession with Orthodoxy, though.
So for R' Student, it's a way to disenfranchise a subgroup of Modern Orthodoxy, while claiming that Post-O is not necessarily Non-O. For R' Woolf, it's a symptom of the rise of textualism over mimeticism, and a drawing away from a concern with avodat Hashem. R' Woolf's Post-O are, apparently, still Orthodox, but not in modes based on tradition. R' Brill's Post-O are individuals, not a sociological subgroup, who have consciously left Orthodoxy after choosing to enter it. So for him, Jews can be Post-O only by virtue of having become Non-O.
Whose Vision Reigns Supreme?