Abbreviations:
NDT: Neo-Darwinian Theory
CA: Common Ancestry
RSM: Random, Spontaneous Mutations
NS: Natural Selection
NREH: Non-Random Evolutionary Hypothesis
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Darwinism's Debit Sheet: 23 items

On the Origin of Skeptics:
If it could be demonstrated that any complex organ existed, which could possibly have been formed by numerous, successive, chance-driven, slight modifications, my skepticism would absolutely break down. (Charles Darwin, perturbed by ASL, 2004)

"...the theory of NS.... is now the prevailing explanation of evolutionary change. It must be admitted, however, that it has achieved this position less by the amount of irrefutable proofs it has been able to present than by the default of all opposing theories." (Mayr, 1988)

1. To the question What is the NDT?, different Darwinists give different answers .
2. To the question What is NS?, different Darwinists give different answers .
3. The feasibility of the idea that RSM + NS can lead to macroevolution has never been demonstrated.

      In his book Darwin on Trial (1991), Phillip Johnson made the following statements:
"The hypothesis that NS has the degree of creative power required by Darwinist theory remains unsupported by empirical evidence" (p.98);
 "...positive evidence that Darwinian evolution either can produce or has produced important biological innovations is non-existent" (p.115);.
"NS exists, to be sure, but no one has evidence that it can accomplish anything remotely resembling the creative acts that Darwinists attribute to it" (p.115).
These statements (if true) are clearly devastating to Darwinism. In his 4-page review of this book, Stephen Gould (1992) would surely have shown them to be false, if he could have done so. He didn't; therefore, he couldn't.

4. No NDT based on copying errors can explain convergent evolution (Spetner, p.110).
5. Mutations leading to bacterial resistance to streptomycin cannot be typical of mutations needed for the NDT. (Spetner, p. 141)
6. The kind of mutations required by the NDT have never been observed. (Spetner, p. 179)
7. Population changes observed in Reznick's guppies are too rapid to be explained by the NDT. An NREH is more plausible. (Spetner, p. 206)
8. RSM + NS cannot explain the origin of cilia, bacterial flagella, blood clotting and other irreducibly complex systems (Behe, pp. 65, 72, 87).
9. The Cambrian Explosion fossil record is incompatible with NDT (Johnson, p. 54; Wells, p.41). "The problem of the Cambrian explosion has not yet been solved" (Futuyma, p174).
10. Available molecular evidence has failed to confirm CA or NDT (Johnson, p.101).
11. NDT does not explain the development of homologous organs not controlled by the same genes (Wells, p. 77).
12. NDT cannot explain the development of male peacock tails (Macbeth, pp. 82 - 85).
13. RNA virus studies show that time plus the availability of mutations are not sufficient conditions for continuous evolution (Larson, p. 174).
14. There is no persuasive evidence that changes observed in UK populations of light and dark peppered moths are evidence for NDT (Wells, p153).
15. Galapagos finches' beak sizes have oscillated with time, showing no monotonic evolutionary trend (Wells, p. 169).
16. Phenotypic plasticity (Spetner, p. 199): many organisms change through environmental triggers and demonstrate adaptability at the single organism level; the NDT assigns adaptability to the population level.
17. Darwin used "bait and switch" tactics: he started discussing the need to explain complexity increases (in the evolution of the human eye) and switched immediately to discussing adaptivity increases. Adaptivity increases do not entail complexity increases (cf. item 5. above).
18. Molecular phylogeny gives internally inconsistent evidence in regard  to CA (Wells, p. 49).
19. The presence of identical genes in cells that differ radically from one another (the "genomic equivalence" paradox) (Wells, p.191).
20. Darwinists have published no comprehensive reviews that give critical, up-to-date assessments of the strengths and weaknesses of the NDT in the light of all the available evidence and analyses.
21. The NDT, as applied to previous processes involving the generation of new  characters, is untestable and unfalsifiable.
22. No evidence has been published showing that any new character has ever appeared through RSM and NS alone.
23. Darwin used false advertising: "...Darwin, whose book The Origin of Species is not really on that subject.." (Simpson, p.81)

References

Michael J. Behe (1996) Darwin's Black Box: the Biochemical Challenge to Evolution (Simon and Schuster, New York, NY)
Douglas J. Futuyma (2003) Evolutionary Biology (Sinauer Associates,Sunderland, MA, 3rd edition, 1998).
Stephen Jay Gould (1992) Scientific American 267, 118-121.
Phillip E. Johnson (1991) Darwin on Trial  (1st edition, Regnery Gateway, Washington DC)
Phillip E. Johnson (1993) Darwin on Trial  (2nd edition, InterVarsity Press, Downers Grove, Illinois)
Ronald G. Larson (2000) Viral Evolution: Climbing Mount Molehill? Perspectives on Science and Christian Faith 52 (3) 169-180
Norman Macbeth (1971) Darwin Retried: an Appeal to Reason, Harvard Common Press)
Ernst Mayr (1988) Toward a New Philosophy of Biology ( Belknap Press of Harvard University Press, Cambridge MA)
George Gaylord Simpson (1964) This View of Life: the Wordl of an Evolutionist (Harcourt, Brace & World, New York)
Lee Spetner (1997, 1998) Not by Chance! Shattering the Modern Theory of Evolution (Judaica Press, Brooklyn, NY)
Jonathan Wells (2000) Icons of Evolution: Science or Myth? (Regnery Publishing, Washington, DC)