Taxononmy is classification. It by definition cannot be error because it is subjective. While one could say that our system is much more precise than the ancients, one must never confuse accuracy and precision, especially in situations where, as here, the issue is one of inherent definitions.
It would also be obvious to God that insects have six legs, not four, and that rabbits do not chew their cud.
Now, why would God indulge these misconstructions and not set those Iron Age goatherders straight? Why is it that God did not seem to know any more than the folks writing about Him?
To some extent. The criteria for classification can be arbitrary but, given them, taxonomy is only subjective to the extent that the things being classified fit into more than one category: is Archeopteryx more like a bird or a dinosaur? Is "Lucy" more like a modern ape or a modern person?
In biology, there is one true, non-subjective, classification: the one given by the phylogenetic tree. Cladistic analysis, especially that based on genetic traits, has allowed us to fill in some parts unambiguously: people and chimps have a fairly recent common ancestor, people-chimps-gorillas an older one, people-chimps-gorillas-orangutans an even more ancient one, etc.
A possible way to falsify evolution would be to find things that simply cannot be classified under this scheme.
Does anyone know whether Aristotle classified bats as mammals?
The 4-legged insect has nothing to do with taxonomy.