If I understand your response, it can be boiled down to this:
(1) TOE is dependent upon "natural law" for the cause.
(2) Natural law in this context can be defined to be mutations.
(3) Ergo, mutation drives TOE.
But where is the evidence for this? Since almost all mutations cause negative effects, where is the demonstrated "increased fitness"? Remember, "fitness" is defined as: increased number of offspring, or greater survival ability of offspring, or both. (That's not my definition, that's the accepted definition of fitness which arose, I think, to counter the tautology problem of the "Survival of the Fittest" phrase.)
You are begging the question when you assert: "...it is known why an apparent mutation (i.e. a difference between chimps and man) would be advantageous" since you have not demonstrated that those differences are in fact due to mutation as the causative factor. Your argument here boils down to:
(A) Mutation causes genetic change.
(B) We see differences between similar species.
(C) Therefore, these differences have been caused by mutation.
Again, this is reasoning "by induction". Which is weak. Yes, there is evidence of mutation. But evidence that mutation works to produce "fitter" critters is lacking, I assert. And the whole TOE hangs upon this one point.
Great post. It also needs to be added that evolution depends on a whole series of successively beneficial mutations. The vast preponderance of harmful mutations over beneficial ones (admitted to even by the most ardent evolutionists) makes the odds of achieving successively beneficial ones astronomical in just a single instance. To achieve them in the miriads of times it would have had to occur to turn bacteria into men, would be totally impossible.
Consider the case of sickle-cell and thalassemia. These are two different mutations of one of the genes responsible for hemoglobin. Sickle-cell is found in equatorial Africa, and thalassemia around the Mediterranian.
If you have two copies of the sickle-cell gene, you have the disease sickle-cell anemia, and are much less likely to pass your genes on. Ditto for thalassemia.
But if you just have one copy of the gene, you have no ill effects. However, you are also resistant to malaria.
And so, in true Darwinian fashion, the genes are found in a large proportion of people in malarial zones, and are very rare elsewhere.
Are these mutations beneficial or not? The answer depends on how much malaria is in your environment.
Your original request for a falsification of common descent has morphed into your current argument that we cannot assume mutations are responsible for driving evolution.
It is safe to assume that the phenotypic differences between organisms is due to mutation. An example of this are a group of genes found in virtually all multicellular organisms called the Hox cluster. This locus is a major determinant of the overall body plan of the animal. It looks like it went through several duplication events throughout evolutionary history. This is still an area of active research, but where it has been tested, the mutations to the Hox cluster have been experimentally verified to be responsible for the visible changes of the organism (i.e. more legs, wings etc). There are many other genes that are common to different critters where it can be showed that the specific mutation involved leads to the change in phenotype.