Summary of problems:
Explore Evolution asserts that "this book will help you understand why many scientists find [contemporary Darwinian theory] persuasive, and why other scientists question key aspects of it" (p. v). The supposedly "key aspects" or "key claims" which Explore Evolution targets are issues that are not scientifically controversial, yet are persistent targets of creationist attack. Biologists have reached a strong consensus about the validity of universal common descent, the power of natural selection, and the importance of studying fossils, embryology, biogeography, homologous structures, etc. There is ongoing research and disagreements concerning the details in all these areas. However, Explore Evolution implies that any controversy or disagreements within evolutionary biology casts doubt on the underlying validity of the theory of evolution. This is a classic creationist falsehood.
Full discussion:
The preface states
We hope this book will help you understand what contemporary Darwinian theory is, why many scientists find it persuasive, and why other scientists question key aspects of it.Explore Evolution, preface
If we assume that this statement is referring to scientists in fields with some relevance to evolutionary theory (e.g. biologists, geologists, anthropologists etc.), this statement cannot be supported. Nearly every relevant national and international scientific organization has taken a position in favor of the basics of evolutionary theory, and in opposition to creationism and intelligent design. This February 2006 statement from the American Association for the Advancement of Science, the largest general scientific society in the world (serving 262 affiliated scientific societies and academies, with over 10 million members), is only one example of many.
Evolution is one of the most robust and widely accepted principles of modern science. It is the foundation for research in a wide array of scientific fields and, accordingly, a core element in science education. The AAAS Board of Directors is deeply concerned, therefore, about legislation and policies recently introduced in a number of states and localities that would undermine the teaching of evolution and deprive students of the education they need to be informed and productive citizens in an increasingly technological, global community. Although their language and strategy differ, all of these proposals, if passed, would weaken science education. The AAAS Board of Directors strongly opposes these attacks on the integrity of science and science education. They threaten not just the teaching of evolution, but students' understanding of the biological, physical, and geological sciences.
Some bills seek to discredit evolution by emphasizing so-called "flaws" in the theory of evolution or "disagreements" within the scientific community. Others insist that teachers have absolute freedom within their classrooms and cannot be disciplined for teaching non-scientific "alternatives" to evolution. A number of bills require that students be taught to "critically analyze" evolution or to understand "the controversy." But there is no significant controversy within the scientific community about the validity of the theory of evolution. The current controversy surrounding the teaching of evolution is not a scientific one.(AAAS Statement on the Teaching of Evolution, 2006), emphasis added
In contrast, the Discovery Institute lists only 700 scientists on their Dissent from Darwin statement. No scientific societies have signed on to that statement. Many of the signers do not have degrees or research interests in relevant scientific disciplines. Not surprisingly, the Dissent from Darwin list has many names of engineers and computer scientists, whose everyday work does not bring them in contact with modern evolutionary theory. This number of dissenters, even if they were all working in a relevant scientific field, is certainly small when compared to the hundreds of thousands of scientists affiliated with the scientific societies which have passed statements or resolutions supporting modern evolutionary theory. It is even small compared to the number of graduate students in science and engineering disciplines. According to the National Science Foundation, institutions of higher education in the USA alone produce over 20,000 doctoral graduates in science and engineering annually.
So while it is certainly true that "some scientists" question evolution, hardly any working scientists in the relevant disciplines find it to be controversial, and no relevant scientific society finds it to be controversial. The perception left by this statement in Explore Evolution is completely wrong.
It would fair to say that there are debates and controversies within evolutionary biology over questions such as the relative importance of natural selection and neutral mutations to evolutionary change, the role of symbiosis, or the nature of large-scale patterns of evolutionary change. These questions, though, are not the discussed in Explore Evolution. The supposedly "key aspects" of the theory which Explore Evolutionclaims to present "both sides" of are, in fact, simply repetitions of long-discredited creationist claims, as will be shown throughout this critique.