Summary of problems:

This claim has a long history in the creationist literature, but is uniformly rejected by biologists as rooted in basic misunderstandings. The apparent homology of a single trait would not be treated as evidence of common descent. By examining multiple traits, all showing the same nested hierarchy of modifications of a common starting point, scientists can test hypotheses about common descent. There is nothing circular about this process.

Full discussion:

The argument that homology is defined in a circular manner was a centerpiece of Jonathan Wells's creationist book Icons of Evolution. Wells, an uncredited co-author of EE, undertook graduate studies in biology at the behest of his religious leaders. He explained to a Unification Church ("Moonie") publication "Father [Sun Myung Moon]'s words, my studies, and my prayers convinced me that I should devote my life to destroying Darwinism."

EE reuses Wells's figure 4.1 as its figure 2:1, merely adding color to the figure. Similarly, the discussion of homology as a circular argument is a lightly rewritten version of what Wells wrote. Compare EE:

Some biologists suggest that the problems of understanding homology stem from Darwin himself, who re-defined homology as the result of common ancestry.

This made the concept of homology circular, say many critics. If homology is defined as "similarity due to common descent," then to say that homology provides evidence for common descent is to reason in a circle.

EE, p. 49

Wells writes:

before Darwin (and for Darwin himself), the definition of homology was similarity of structure and position …. But similarity of structure and position did not explain the origin of homology, so an explanation had to be provided.
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But for twentieth-century neo-Darwinists, common ancestry is the definition of homology as well as its explanation.
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[E]volution was a theory, and homology was evidence for it. With Darwin's followers, evolution is assumed to be independently established, and homology is its result. The problem is that now homology cannot be used as evidence for evolution except by reasoning in a circle.

Jonathan Wells (2000) Icons of Evolution, Regnery Publishing, Inc.:Washington, DC. pp. 62-63

The restatement of these claims in EE does not require any different response than Wells received, since it adds nothing to the argument. Reviewer Alan Gishlick responded to Wells's treatment of homology:

Wells claims that homology is used in a circular fashion by biologists because textbooks define homology as similarity inherited from a common ancestor, and then state that homology is evidence for common ancestry. Wells is correct: this simplified reading of homology is indeed circular. But Wells oversimplifies a complex system into absurdity instead of trying to explain it properly. Wells, like a few biologists and many textbooks, makes the classic error of confusing the definition of homology with the diagnosis of a homologous structure, the biological basis of homology with a procedure for discovering homology. In his discussion, he confuses not only the nature of the concept but also its history; the result is a discussion that would confuse. What is truly important here is not whether textbooks describe homology circularly, but whether homology is used circularly in biology. When homology is properly understood and applied, it is not circular at all.
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Today, biologists still diagnose homologous structures by first searching for structures of similar form and position, just as pre-Darwinian biologists did. (They also search for genetic, histological, developmental, and behavioral similarities.) However, in our post-Darwin period, biologists define a homologous structure as an anatomical, developmental, behavioral, or genetic feature shared between two different organisms because they inherited it from a common ancestor. Because not all features that are similar in two organisms are necessarily inherited from a common ancestor, and not all features inherited from a common ancestor are similar, it is necessary to test structures before they can be declared homologous. To answer the question, "could this feature in these groups be inherited from a common ancestor?" scientists compare the feature across many groups, looking for patterns of form, function, development, biochemistry, and presence and absence.
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If, considering all the available evidence, the distribution of characteristics across many different groups resembles a genealogical pattern, it is very likely that the feature reflects common ancestry. Future tests based on more features and more groups could change those assessments, however — which is normal in the building of scientific understanding. Nevertheless, when a very large amount of information from several different areas (anatomy, biochemistry, genetics, etc.) indicates that a set of organisms is genealogically related, then scientists feel confident in declaring the features that they share are homologous. Finally, while judgments of homology are in principle revisable, there are many cases in which there is no realistic expectation that they will be overturned.

So Wells is wrong when he says that homology assumes common ancestry. Whether a feature reflects common ancestry of two or more animal groups is tested against the pattern it makes with these as well as other groups. Sometimes, though not always, the pattern reflects a genealogical relationship among the organisms — at which point the inference of common ancestry is made.
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Evolution and homology are closely related concepts but they are not circular: homology of a structure is diagnosed and tested by outside elements: structure, position, etc., and whether or not the pattern of distribution of the trait is genealogical. If the pattern of relationships looks like a genealogy, it would be perverse to deny that the trait reflects common ancestry or that an evolutionary relationship exist between the groups. Similarly, the closeness of the relationship between two groups of organisms is determined by the extent of homologous features; the more homologous features two organisms share, the more recent their common ancestor. Contrary to Wells's contention, neither the definition nor the application of homology to biology is circular.
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Some formulations of the concept of homology appear to be circular, but as discussed above, because there is an external referent (the pattern that characteristics take across groups) that serves as an independent test, the concept, properly defined and understood, is not. Wells's claim that homology is circular reveals a mistaken idea of how science works. In science, ideas frequently are formulated by moving back and forth between data and theory, and scientists regularly distinguish between the definition of a concept and the evidence used to diagnose and test it.

Alan Gishlick (2001) Icons of Evolution? Why Much of What Jonathan Wells Writes about Evolution is Wrong, National Center for Science Education: Oakland, CA. 64 p.

Gishlick here is using "homologous features" in the sense of a "shared derived character," as discussed above. There are several important points that bear emphasizing.

First, biologists do not look at only one line of evidence to infer common descent; it is the agreement of multiple lines of evidence about morphological, genetic, behavioral, ecological and developmental similarity which allows that inference.

Second, that inference is a testable hypothesis. The addition of new lines of evidence allows a test of evolutionary hypotheses. For instance, biologists will test evolutionary hypotheses produced based on skull morphology with information from the DNA sequence of a particular gene. A common test for the accuracy of an evolutionary inference is to run the same analysis while excluding part of the data, and using those excluded data to confirm the accuracy of the results.

Third, the hypothesis of homology (which follows from an evolutionary hypothesis) is testable. In reconstructions of the common ancestry of a group, it is not uncommon to find that certain traits evolved more than once, or appear and disappear at various points on the tree. Those characters are then subject to greater scrutiny, since their disagreement with other traits suggests that there may be more that needs to be understood about that trait. Some traits which appear similar are deemed not to be homologous as a result of this analysis, but to be the result of parallel evolutionary pressure.

Fourth, the evolutionary hypothesis can be tested by reference to previously unexamined species. If the evolutionary hypothesis is correct, new species ought to fit easily into the pattern predicted. Since the evolutionary hypothesis is based on nested groups sharing certain novel traits, that hypothesis would be challenged if newly described species had a mosaic of traits that did not fit into that nested hierarchy.

Explore Evolution, like other creationist books before it, makes the mistake of treating the structures of organisms in isolation. While it would be circular to use a single trait to infer an evolutionary history and then to use that history to infer the common ancestry of that trait, scientists do not do that. In presenting homology and common descent as a circular construct misused by scientists, EE misinforms students about basic concepts, bringing confusion rather than clarity.

Scientists build on earlier hypotheses with new data, and build new hypothesis from that new data. This advance in knowledge adds a third dimension to what EE treats as two-dimensional. Rather than a flat circle, the scientific process spirals upward.