For any not familiar with the infamous work, these lines from near the paper's end give the flavor of the presentation:
"Thus, a liberatory science cannot be complete without a profound revision of the canon of mathematics. As yet no such emancipatory mathematics exists, and we can only speculate upon its eventual content. We can see hints of it in the multidimensional and nonlinear logic of fuzzy systems theory; but this approach is still heavily marked by its origins in the crisis of late-capitalist production relations. Catastrophe theory, with its dialectical emphases on smoothness/discontinuity and metamorphosis/unfolding, will indubitably play a major role in the future mathematics; but much theoretical work remains to be done before this approach can become a concrete tool of progressive political praxis. Finally, chaos theory -- which provides our deepest insights into the ubiquitous yet mysterious phenomenon of nonlinearity -- will be central to all future mathematics."It may be best to start by reading Sokal's explanation for perpetrating the hoax in the first place, before actually reading the fraudulent paper itself.
The original paper in its entirety, is here.
And much further discussion and follow-up can be linked to from this Sokal webpage:
Alan also authored an entire book, "Beyond The Hoax," about the whole affair.
And, all-in-all, I'm not so sure that much has changed in the dozen years passed since the hoax's unveiling --- indeed, the public's comprehension of science today may be even worse than before :-(