As other PT contributors have already shown, there are many problems with Meyer’s peer reviewed contribution. I intend to share my research findings here on PT over the coming days as I have researched close to half a dozen claims and references so far.
Meyer when discussing  the Cambrian period states the following
One way to estimate the amount of new CSI  that appeared with the Cambrian animals is to count the number of new cell types that emerged with them (Valentine 1995:91–93).
The full reference reads: Valentine, I. W. 1995. Late Precambrian bilaterians: grades and clades. Pp. 87–107 in W M. Fitch and FJ. Ayala, eds., Tempo and mode in evolution: genetics and paleontology 50 years after Simpson. National Academy Press, Washington, D.C..
The paper also appeared in PNAS as: Valentine, J.W. 1994. Late Precambrian bilaterians: grades and clades. Proc Natl Acad Sci U.S.A. July 19; 91 (15): 6751-6757.
Notice my surprise when I thus read
Cell-phenotype numbers in living phyla, and a model of cell-phenotype number increase, suggest an origin of metazoans near 600 my ago, followed by a passive rise in body-plan complexity. Living phyla appearing during the Cambrian explosion have a Hox/HOM gene cluster, implying its presence in the common ancestral trace makers. The explosion required a repatterning of gene expression that mediated the development of novel body plans but evidently did not require an important, abrupt increase in genomic or morphologic complexity.
But perhaps the measure used by Valentine would give some support to Meyer’s arguments?
At present there is no evidence of a major step in body-plan complexity during the Cambrian explosion.
So why would Meyer quote Valentine as supportive of Meyer’s claim that
The Cambrian explosion represents a remarkable jump in the specified complexity or “complex specified information” (CSJ) of the biological world.
When the actual paper does not lend much support to such a thesis.
Del Ratzsch author of Nature, Design and Science remarked
“I think that some are certainly too far in the materialist direction, and they claim that science backs them up on that. ID can at least serve a ‘keeping em’ honest’ function, even if nothing else. I think that ID may very well have things to offer science, but I think that it is too early for ID to claim that it has done so. I don’t think that it is just obvious that ID will contribute substantively to science, but I think it has that potential, and that it should be pushed as far as it can be made to legitimately go.”
In order for ID to live up to Del Ratzsch’s expectations it needs to do a lot of work. So far it fails even the minimal qualifications of performing a ‘keeping em’ honest’ function. Let’s not hold our breath for ID contributing something substantively to science.
 Stephen C. Meyer, The origin of biological information and the higher taxonomic categories, PROCEEDINGS OF THE BIOLOGICAL SOCIETY OF WASHINGTON 117(2):213-239. 2004
 As others already have shown, Meyer makes no attempt to show that his concept of CSI has any relevance to a similarly named concept found in the works of William Dembski.
As is typical (see (Pennock ) with Meyer, this is a verbatim quote of an earlier paper by Meyer, Ross and Chien “The Cambrian Explosion: Biology’s Big Bang”.
 See Pennock DNA by Design?: Stephen Meyer and the Return of the God Hypothesis. In Ruse, Michael and William Dembski (eds) Debating Design. New York: Cambridge University Press for more examples of how Meyer recycles his claims.)
One way to measure the increase in specified information or specified complexity of the animals that appeared in the Cambrian is to assess the number of cell types that are required to build such animals and to compare that number with those creatures that went before. 25
Julián Monge-Nájera1 and Hou Xianguang, isparity, decimation and the Cambrian “explosion”: comparison of early Cambrian and Present faunal communities with emphasis on velvet worms (Onychophora)
We conclude that (1) a mature ecological community structure was generalized during the Cambrian, and even biodiversity and equitability indices were surprisingly close to modern values; (2) the morphological diversity and geographic distribution of onychophorans indicate a significant pre-Cambrian evolutionary history which does not support the “explosion” hypothesis; (3) disparity among phyla was not as important as the explosion-decimation model predicts, but in the case of onychophorans, disparity within the phylum was greater than it is today and its reduction may have been associated with migration into the sediment when large predators evolved.
James W. Valentine1, David Jablonski and Douglas H. Erwin, REVIEW ARTICLE Fossils, molecules and embryos: new perspectives on the Cambrian explosion Development 126, 851-859 (1999)
James W. Valentine, PRELUDE TO THE CAMBRIAN EXPLOSION, Annual Review of Earth and Planetary Sciences May 2002, Vol. 30, pp. 285-306
Abstract The Prelude began with the origin of Metazoa, perhaps between 720 and 660 million years ago (mya), and ended with the geologically abrupt appearance of crown bilaterian phyla that began between 530 and 520 mya. The origin and early evolution of phyla cannot be tracked by fossils during this interval, but molecular phylogenetics permits reconstruction of their branching topology, whereas molecular developmental evidence supports hypotheses for the evolution of the metzoan genome during the rise of complex bodyplans. A flexible architecture of genetic regulation was in place even before the appearance of crown sponges, permitting increases in gene expression events as bodyplan complexity rose. Neoproterozoic bilaterians were chiefly small-bodied but likely diverse, whereas in the earliest Cambrian, between 543 and approximately 530-520 mya, bodies that were complex by marine invertebrate standards evolved in association with body-size increases.
JAMES W. VALENTINE and DAVID JABLONSKI Morphological and developmental macroevolution: a paleontological perspective, Int. J. Dev. Biol. 47: 517-522 (2003)
ABSTRACT Evidence of the morphological evolution of metazoans has been preserved, in varying degrees of completeness, in the fossil record of the last 600 million years. Although extinction has been incessant at lower taxonomic levels, genomic comparisons among surviving members of higher taxa suggest that much of the developmental systems that pattern their bodyplans has been conserved from early in their history. Comparisons between the origin of morphological disparity in the record and patterns of genomic disparity among living taxa promise to be interesting. For example, Hox cluster composition varies among major taxa, and the fossil record suggests that many of the changes in Hox clusters may have been associated with late Neoproterozoic evolution among minute benthic vermiform clades, from which crown bilaterian phyla arose just before or during the Cambrian explosion. Study of genomic differences among crown classes and orders whose timing and mode of origin can be inferred from morphological data in the fossil record should throw further light on the timing and mode of origin of genomic disparities.