What are the requirements for 'knowing better?' Seriously. I'd like to read the book, but if it requires an extensive knowledge of mathematics to understand, I'm out.
Well, perhaps that is part of the problem. For a rigorous reference of any matter regarding information theory as it is frequently used in these forums, the book that is the defacto gold standard in mathematics is "Kolmogorov Complexity and its Applications" by Li and Vitanyi. It is well-known, highly regarded, and contains everything you need to know to make Dembski's flaws transparent. Mathematics is not science; if you accept the axioms, you have to accept everything derived from those axioms. I am highly skeptical of anybody who "reinvents" mathematics that contradict texts from reputable mathematics publishers such as Springer-Verlag. Unless they can demonstrate a flaw in the original derivation of the mathematics, they necessarily must throw out all mathematics as we know it, a step no one seems prepared to do. Dembski treats math like science, thinking that he can tweak the parts he doesn't like without having to throw everything out. This fact itself discredits him, nevermind the fact that his ideas don't really make any sense mathematically and are internally inconsistent if scrutinized rigorously. But as you point out, most people really aren't in a position to make a critical evaluation of all but the most trivial mathematical concepts.
However, no really rigorous math text is easy for the layman to absorb. The Li and Vitanyi book mentioned above is much easier to read than most (it is regularly used as a text for math post-grads), but it would still give most non-matheticians a "deer in the headlights" look by the end of the first chapter. Its like engineering: if you could learn it in a matter of months, people wouldn't be spending several years studying full-time just to get an entry-level amount of knowledge.