I agree entirely with another review that said this is entertaining and insightful, but with sadly many mistakes. While agreeing with everyone elses quoted mistakes, I thought I would add to the catalogue.
Homeopathic dilutions. The general statement that Whyte makes that homeopathic dilutions can be so dilute they are extremely unlikely to contain even a single molecule of the solute, is correct, but the specific example he gives is arithmetically wrong. In an X20 solution, 1cc of solution would contain 10 to 100 molecules of the solute, if we take the solute to have a molecular weight of 60 to 600g/mol, a plausible range for a nature-derived chemical. Although for a macro-molecule like a protein, with much larger molecular weight over 6000g/mol, then there would be on average fewer than one left in 1cc. 1cc is a small quantity; if we are interested in proving none left in larger quantities, then rather larger dilutions are required.
The Trinity. Whyte argues that the Trinitarian Christians' doctrine that God is Three and God is One must be false, by appealing, it appears, to axiomatic set theory. I think it is actually just a pedant's joke. I think Trinitarians are guilty of no more than Humpty-Dumpty-speak ("a word means what I say it means"). There are plausible alternative interpretations of what Trinitarians mean when they say that, which are consistent with axiomatic set theory, and reflect more closely what they actually mean. In other words, Whyte is forcing on them a kind of "contractual interpretation" of their metaphorical words to impose upon them a belief they don't in fact have. A classic straw man argument that he so deplores.
Popper and the falsity of God. Whyte wrongly implies that the Popperian notion of a theory takes the position that an untestable theory is a false theory. (Popper coined the horrible word "unfalsifiable" instead of "untestable", a bad PR move; but, along with many I prefer to use the synonym "untestable", whose meaning is clear.) Whyte goes on to argue that since the existence of God (provided one says little more than that) is an untestable theory, it must be wrong. This is a misunderstanding of what Popper said, as well as being logically wrong - and Popper was nothing if not logically rigorous. Indeed I agree with Popper himself that the Popperian notion of a theory is not so much a philosophy as a logical necessity. Sadly, it is not uncommon for professional philosophers to misunderstand what Popper meant here, probably because many professional philosophers lack sufficient understanding of science. What Popper actually says is that an untestable theory is (a) vacuous, since it makes no prediction, so in a scientific sense we don't need it - - and (b) not a theory at all, rather a belief, tautologically, since it is untestable. In other words, all Popper tells us is that belief in a God is religion not science, which I think we already knew. That is why "creation scientists" get up real scientists' noses so much. Richard Dawkins is much better on this. He distinguishes carefully between deist and theist notions of religion, deism being the vacuous belief "there is a god, he created the universe and its laws" and no more; whereas theism (additional beliefs such as those in the bible/koran) adds a lot of magical baggage which typically becomes testable and hence inconsistent with science. Dawkins understands perfectly that the deist position is logically unimpeachable, and restricts his arguments to theists who believe a lot more. Compare this with the situation in Axiomatic Set Theory, the basic axioms of mathematics, (which Whyte implicitly uses). The Axioms are (tautologically) untestable. But it doesn't mean that these axioms are "false". If that were so, we would get a contradiction from using them, and we don't. We can even pick and choose which axioms we like, as with different geometries using different axioms.