According to the online critique of Explore Evolution by the National Center for Science Education:
(A) EE claims that natural selection produced only oscillations in beak size in Galápagos finches, but “in the course of a few years, the size changes within species were large enough to explain the differences among the various species of Galápagos finches,” and “the size and shape of finch beaks did change over the course of the 30 years that biologists have been studying the populations.” 
(B) EE claims that Galápagos finch species are merging rather than diversifying, but “the hybridization observed in the finches is not enough to merge two species, and observations in the field have actually shown substantial evidence of incipient speciation.” Furthermore, EE “introduces an extrapolation which bears no resemblance to what any scientist has predicted.” 
A. Oscillations in Beak Size
Contrary to the NCSE Critique, EE actually does acknowledge that beak length in one species “showed a slight net increase.” (EE, p. 93) The question is whether the increase could “explain the differences among the various species of Galápagos finches,” as the NCSE claims.
The answer is no. Selection for beak size alone cannot explain the differences among various species of finches, any more than selection for tail size alone can explain the differences among various species of cats. Differences in beak morphology are not the only distinguishing feature among the various species of Galápagos finches. As the NCSE Critique itself acknowledges, songs are another distinguishing feature, and there may well be more. 
None of the evidence from the Galápagos finches gives us any reason to believe that natural selection can accomplish more than artificial selection–and the latter has never been observed to produce a new species. In 1997, evolutionary biologist Keith Stewart Thomson wrote: “A matter of unfinished business for biologists is the identification of evolution’s smoking gun,” and “the smoking gun of evolution is speciation, not local adaptation and differentiation of populations.” Before Darwin, the consensus was that species can vary only within certain limits; indeed, centuries of artificial selection had seemingly demonstrated such limits experimentally. “Darwin had to show that the limits could be broken,” wrote Thomson, “so do we.” 
The burden is not on critics of Darwinism to show that there are limits to natural selection. Hundreds of years of domestic breeding, and decades of laboratory and field studies on wild populations, indicate that there are such limits.  The burden of proof is on Darwinists who claim that natural selection can go beyond those limits. Certainly, the beak changes that have been observed in the Galápagos finches fall far short of providing that proof.
B. Hybridization and Extrapolations
The hybridization currently observed in the finches may or may not be enough to merge two species; nobody really knows. After 1983, Peter and Rosemary Grant and their colleagues noticed that several finch species on one island were producing hybrids that thrived and reproduced. In fact, the hybrids did better than their parent species. The Grants predicted that this process, if unchecked, “should lead to fusion of the species into one population.” This would not happen overnight: Extrapolating from the observed frequency of hybridization, the Grants estimated that it would take 100 to 200 years for these species to merge completely. 
The NCSE critique claims that EE “introduces an extrapolation [on page 92] which bears no resemblance to what any scientist has predicted,” but the NCSE’s claim is false. In 1991, Peter Grant estimated the number of “selection events” (such as changes in beak depth during a drought) required to transform the medium ground finch into another species: “The number is surprisingly small: about 20 selection events would have sufficed. If droughts occur once a decade, on average, repeated directional selection at this rate with no selection in between droughts would transform one species into another within 200 years.” A 1999 booklet published by the U. S. National Academy of Sciences repeated the extrapolation: “If droughts occur about once every 10 years on the islands, a new species of finch might arise in only about 200 years.” 
So by extrapolating from processes observed in the present, Grant derived two contradictory predictions: In 200 years, unchecked selection for larger beaks could produce divergence into separate species, or unchecked hybridization could produce the opposite. Yet these are predictions, not evidence. In fact, the fluctuating climate of the Galápagos suggests that neither process is likely to continue indefinitely, and the Grants concluded that “over the long term there should be a selection-hybridization balance.” 
According to the NCSE Critique, field observations of the Galápagos finches show “substantial evidence of incipient speciation.” But “incipient species” is nothing more than a prediction based on Darwin’s theory. In The Origin of Species Darwin wrote: “According to my view, varieties are species in the process of formation, or are, as I have called them, incipient species.”  Defining varieties as “incipient species” assumes that they are their way to becoming separate species. But without actually observing it we have no way of knowing whether two varieties will continue to diverge until they become distinct species, whether they will continue indefinitely as varieties of the same species, or whether they will merge through hybridization.
The National Academy booklet cited above (which lists NCSE Executive Director Eugenie Scott as a member of its steering committee) claims that the finches are “a particularly compelling example” of the origin of species.  As we saw above, however, no new species have been observed to originate from selection on finch beaks. The National Academy booklet’s exaggeration goes far beyond the evidence.
The scientific literature actually contains no confirmed reports of instances in which new species were observed to originate by variation and selection. British bacteriologist Alan H. Linton went looking for direct evidence of speciation and concluded in 2001: “None exists in the literature claiming that one species has been shown to evolve into another. Bacteria, the simplest form of independent life, are ideal for this kind of study, with generation times of twenty to thirty minutes, and populations achieved after eighteen hours. But throughout 150 years of the science of bacteriology, there is no evidence that one species of bacteria has changed into another… Since there is no evidence for species changes between the simplest forms of unicellular life, it is not surprising that there is no evidence for evolution from prokaryotic [e.g., bacterial] to eukaryotic [e.g., plant and animal] cells, let alone throughout the whole array of higher multicellular organisms.”
The NCSE critique objects to Linton’s statement (which is found on pages 104-105 of EE) on the grounds that it “misrepresents what evolutionary biology actually holds.” But Linton’s statement is not about evolutionary biology “holds.” It is about the lack of evidence for what evolutionary biology holds. The NCSE critique objects that EE “ignores the hundreds of papers which address the study of speciation in bacteria,” and it cites as examples two articles published in Science in 2007.  But the articles do not provide evidence that bacteria evolve into new species. One article compares genomes from two existing species to support a hypothesis about how they might have diverged, and the other article describes conceptual models and computer simulations. Both articles simply assume that bacterial species evolve into other species. Linton was right.
As evolutionary biologists Lynn Margulis and Dorion Sagan wrote in 2002: “Speciation, whether in the remote Galápagos, in the laboratory cages of the drosophilosophers, or in the crowded sediments of the paleontologists, still has never been directly traced.”  Evolution’s smoking gun is still missing.
 NCSE, Critique of Explore Evolution. October 2, 2008. “Oscillations.” Available online (2008) at http://ncse.com/creationism/analysis/oscillations; Peter R. Grant and B. Rosemary Grant, “Unpredictable Evolution in a 30-Year Study of Darwin’s Finches,” Science 296 (2002): 707-711.
 NCSE, Critique of Explore Evolution. October 2, 2008. “Modern Galápagos Finches.” Available online (2008) at http://ncse.com/creationism/analysis/modern-galapagos-finches.
 NCSE, Critique of Explore Evolution. October 2, 2008. “Oscillations.” Available online (2008) at http://ncse.com/creationism/analysis/oscillations; Peter R. Grant and B. Rosemary Grant, “Genetics and the origin of bird species,” Proceedings of the National Academy of Sciences USA 94 (1997): 7768-7775. Available online (2008) at http://www.pnas.org/content/94/15/7768.full.
 Keith Stewart Thomson, “Natural Selection and Evolution’s Smoking Gun,” American Scientist 85 (1997): 516-518.
 I. Michael Lerner, Genetic Homeostasis. Edinburgh: Oliver and Boyd, 1954.
 B. Rosemary Grant & Peter R. Grant, “Evolution of Darwin’s finches caused by a rare climatic event,” Proceedings of the Royal Society of London B 251 (1993): 111-117; Peter R. Grant & B. Rosemary Grant, “Hybridization of Bird Species,” Science 256 (1992): 193-197.
 Peter R. Grant, “Natural Selection and Darwin’s Finches,” Scientific American 265 (October, 1991): 82-87; U. S. National Academy of Sciences, Science and Creationism: A View from the National Academy of Sciences, Second Edition. Washington, DC: National Academy of Sciences Press, 1999, p. 11. Available online (2008) at http://www.nap.edu/openbook.php?record_id=6024&page=11.
 Peter R. Grant & B. Rosemary Grant, “Hybridization of Bird Species,” Science 256 (1992): 193-197; Jonathan Wells, Icons of Evolution, Chapter 8.
 Charles Darwin, The Origin of Species, Sixth Edition, p 86. Available online (2008) at http://darwin-online.org.uk/content/frameset?viewtype=side&itemID=F391&pageseq=113.
 U. S. National Academy of Sciences, Science and Creationism, pp. R3, 11. Available online (2008) at http://www.nap.edu/openbook.php?record_id=6024&page=R3
 Alan Linton, “Scant Search for the Maker,” The Times Higher Education Supplement (April 20, 2001), Book Section, p. 29.
 NCSE, Critique of Explore Evolution. October 14, 2008. “Evolving Bacteria.” Available online (2008) at http://ncse.com/creationism/analysis/evolving-bacteria; Christophe Fraser, William P. Hanage, and Brian G. Spratt, “Recombination and the Nature of Bacterial Speciation,” Science 315 (2007): 476-480; Adam C. Retchless and Jeffrey G. Lawrence, “Temporal Fragmentation of Speciation in Bacteria,” Science 317 (2007): 1093-1096.
 Lynn Margulis and Dorion Sagan, Acquiring Genomes: A Theory of the Origins of Species. New York: Basic Books, 2002, p. 32; Wells, The Politically Incorrect Guide to Darwinism and Intelligent Design, Chapter 5.