Explore Evolution claims that some current evolutionary biologists think that mutations that result in major changes in morphology (such as the mutations in the Hox gene Ultrabithorax, which produce the four-winged fruit fly) are necessary to explain morphological evolution. Modern evolutionary biologists do not suggest mutations in the genetic toolkit must have dramatic effects (as discussed elsewhere in this critique). Explore Evolution falsely asserts that evolutionary developmental biologists doubt the role of mutation in development.

The "mutation argument," according to Explore Evolution is:

even if the existing gene pool doesn't supply enough information to build a fundamentally new organism, new mutations can.
Explore Evolution, p. 98

Explore Evolution finds significant problems with this straw man "mutation argument" and implies that "small, limited mutations" are restricted to genes which do not regulate morphology:

Critics of the mutation argument say these textbook examples point to a kind of Catch-22. Small, limited mutations (like those that produce antibiotic resistance) can be beneficial in certain environments but they don't produce enough change to produce fundamentally new forms of life. Major mutations can fundamentally alter an animal's anatomy and structure, but these mutations are always harmful or outright lethal (12) …. That is why critics say mutations have not turned out to be the information-rich super-variations that neo-Darwinian biologists had hoped for.
Explore Evolution, p. 106

To support their case, Explore Evolution cites four papers in reference 11 as critical of the "mutation argument":

Wallace Arthur, "The effect of development on the direction of evolution: toward a twenty-first century consensus." Evolution and Development 6 (2004) 282-288.

K.S.W. Campbell and C.R. Marshall "Rates of evolution among paleozoic echinoderms," in Rates of Evolution, K.S.W. Campbell and M.F. Day eds. (London, Allen and Unwin, 1987).

Eric H. Davidson, Genomic Regulatory Systems, Development and Evolution (San Diego Academic Press, 2001).

Scott F. Gilbert, John M. Opitz, and Rudolf A. Raff "Resynthesizing evolution and developmental biology," Developmental Biology 173 (1996): 357-372.
Explore Evolution, p. 112

Notably, all of the more recent citations (after 1987) are evolutionary developmental biologists and, as we shall see, the citations of their work by Explore Evolution is another example of "creationist abuse of evo-devo."

As Rudolf Raff, a critic of the "mutation argument" (according to Explore Evolution) notes:

There is a whole stable of intelligent design creationist writers associated with the Discovery Institute, and we will see more slick books of bogus science produced to influence the teaching of biology, and even federal funding of research. Evo-devo data have become a part of the creationist rhetorical weaponry, and as evo-devo grows in prominence, the problem will grow in severity
Rudolf Raff, "The Creationist Abuse of Evo-Devo," (2001), Evolution and Development, 3:6, p. 374

Explore Evolution asserts that mutations in the genes regulating development will only produce major mutations that will be harmful. Does Wallace Arthur actually think about mutations that affect development (ontogeny)? Is Arthur a "critic of the mutation argument"?

Subsequent to the modification of a developmental gene (e.g., a Hox gene) by mutation, the ontogenetic trajectory will in many (but not all) cases be reprogrammed so that it follows a different route. The difference may be tiny, moderate, or large.
Wallace Arthur, (2004) "The effect of development on the direction of evolution: toward a twenty-first century consensus." Evolution and Development 6, p. 282

In other words, not all mutations in a developmental gene (a genetic toolkit gene) need have major affects, such as the four-winged fruit fly. Indeed, evolutionary developmental biologists think that relatively modest changes in genes of the genetic toolkit are more likely to prove useful to organisms.

Scott Gilbert is also cited as a "critic of the mutation theory" according Explore Evolution. Gilbert has explained about his view of evolution, (available at National Center for Science Education) in response to misrepresentations of his work by the Discovery Institute in 2002 in their testimony to the Ohio Board of Education.

My research on turtles and my research into evolutionary developmental biology is fully within Darwinian parameters. My gripe has been that neo-Darwinism has supposed that population genetics was the only genetics needed to explain Darwinian evolution. I claim that developmental genetics is also needed. So my research has been to include developmental genetics into the Darwinian mix.
National Center for Science Education (2002), Analysis of the Discovery Institute’s “Bibliography of Supplementary Resources for Ohio Science Instruction”

In contrast to Explore Evolution's misrepresentation, Eric Davidson actually argues that mutations in the "regulatory genome" (CREs and proteins encoded by the genetic toolkit genes) play important roles in animal evolution.

Since the morphological features of an animal are the product of its developmental process, and since the developmental process in each animal is encoded in it's species-specific regulatory genome, then change in animal form during evolution is the consequence of change in genomic regulatory programs for development.
Eric Davidson, in The Regulatory Genome: gene regulatory networks in development and evolution, (2006), p. 27

None of the recent research cited actually undermines what Explore Evolution refers to as "the mutation argument." They all argue that mutations can and do change developmental trajectories, and that these changes are important in our understanding of evolutionary developmental biology. Explore Evolution misleads students by suggesting otherwise.