I fully agree that logical fallacies should be taught, and science class seems to be the most logical (hehe) place for it. As a practical suggestion, using scientific examples of those logical fallacies would probably work really well.
I make the argument that it is impossible that a single bacterium can divide into millions of bacteria in a single day (argument from incredulity). It just doesn't make sense. Can't happen. The students run experiments using different techniques and find, contrary to my protestations, that a single bacterium can produce a million clones of itself in a single 24 hour period. Fallacy exposed.
I make the argument that if light acts as a particle that it can not act like a wave (false dichotomy). The kids run the Young's Double Slit experiment and review the photoelectric effect. Sure enough, light can act as both, a third option that was not inlcuded in the original argument.
I don't see how other classes can lend themselves so easily to demonstrating why these are logical fallacies. A philosophy course would definitely work, but very rarely do high schools have such classes.