The postmodernists worshipped Nietzsche; he was their lodestar. (There are many textual links, but I'm a long way out of grad school—someone else will have to provide them). If you think of Foucault's concentration on the topic of power, that's entirely in the Nietzschean line. The postmodernists were mostly following through on the explosion that Nietzsche and Freud wrought on Western ideas of rationality and objectivity.
I started writing a comment about this when I saw the thread, but could feel it starting to turn into more of an essay, and that's not a good thing at 3am. I remember going to see Derrida when he came to Stanford shortly after 9/11. It was impossible to understand a single thing he was saying—I have a funny story about that for another time. (Edit: turns out I posted it years ago: https://news.ycombinator.com/item?id=341350)
And yet...for all the obscurantism and bullshit, the Sokal hoax and everything else—I came to the conclusion that the postmodernists touched something deeper than their critics, something which we have yet to reckon with.
The real problem with the postmodernists is not that their texts are full of ornate bullshit (look up the story about Searle asking Foucault why he can't just write straightforwardly, and Foucault saying no one in Paris would take him seriously if he did). The real problem is that their program is only negative. Unless I missed it, they never point to anything new.
After deconstructing all the self-contradictory things that humans call knowledge, they have no recommendation for what anybody should actually do. They reach the limits of the human, at which point the only answer is spiritual—but having rejected any possibility of spirit, they end up with nothing. Or, to put it in a different way: deconstruction is fine, but what are you adding? Or another way: criticism, even consummate criticism, isn't enough. (Edit: I found another old comment about this - https://news.ycombinator.com/item?id=713432)
p.s. I didn't answer your question about examples. It's not so easy to give clear examples, because the postmodern analysis isn't definitive on isolated data points—it's more a preponderance-of-the-evidence thing. Also, it's been a large and unspecified number of years since I worked with this material.