Can you briefly explain or point to something brief that explains the specific things that are significantly harmful or incorrect with relation to Descartes' Discourse on Method?

I agree with you that dogmatism is probably a negative thing, unless the dogmatism enforces being non-dogmatic. My shallow reading of Popper and Descartes seems to indicate that they are dogmatic about not being dogmatic, so I really quite like their dogma.

Any other problems with reductionism would be especially interesting.

Any answers to the classic regress argument would also be appreciated, I am not very clever and neither are my acquaintances - we haven't seemed to find anyone to convince us why "A proves B" is epistemically useful...though surely there is some argument

[C PROVES why "A proves B"], and surely some argument

{D PROVES why [C proves why "A proves B"]}, etc.

http://en.wikipedia.org/wiki/Regress_argument

http://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achil...