I found a throw-away critique of Kurt Gödel's Incompleteness Theorem in an essay about Deconstruction:
The basic enterprise of contemporary literary criticism is actually quite simple. It is based on the observation that with a sufficient amount of clever handwaving and artful verbiage, you can interpret any piece of writing as a statement about anything at all. The broader movement that goes under the label "postmodernism" generalizes this principle from writing to all forms of human activity, though you have to be careful about applying this label, since a standard postmodernist tactic for ducking criticism is to try to stir up metaphysical confusion by questioning the very idea of labels and categories. "Deconstruction" is based on a specialization of the principle, in which a work is interpreted as a statement about itself, using a literary version of the same cheap trick that Kurt Gödel used to try to frighten mathematicians back in the thirties.
Now this statement strikes me as perfectly apt, but not sufficiently grounded. I suspect that it's correct, but there isn't enough there to know.
So is the Incompleteness Theorem a "cheap trick" or is it a serious argument that propels philosophy forward? (I presume that the theorem is perfectly valid and valuable in mathematics where it originated.)