Earnshaw's Theorem

My favorite loophole for Earnshaw's theorem is spin-stabilized levitation. It has such an interesting back-story. A 'crackpot' tinkerer invented it, despite physicists telling him it was impossible. It's an impressive accomplishment because the set-up is also very sensitive, so getting it right by trial & error must have taken a lot of persistence. (Once he demonstrate it, physicists were of course able to explain it.) Unfortunately, the inventor got screwed over (or screwed himself, depending on who you ask) on the patent front, and didn't profit from the invention.

For details see: "Spin stabilized magnetic levitation" by Martin, Helfinger, & Ridgway, Am. J. Phys. 65, 4, 1997 http://www.physics.ucla.edu/marty/levitron/spinstab.pdf

This can definitely be a good "bunk science" heuristic along with things like the laws of thermodynamics: If someone is proposing something that seems to break one of these laws/theorems, they'd better (a) realize it, and (b) have a pretty convincing way around it, or some amazing experimental results.

(Note, my work involves magnets and so probably see more than the normal number of crackpot inventors with magnet contraptions).