Good vs Bad in Math of Autism Studies

Ok, so I've been asked to explain the difference between the good math in Shattuck's recent paper about diagnostic substitution, and the Geier's paper on change in autism rates as the use of thimerasol based vaccines has declined.
It's a bit hard to do, because while I have the full text of the Geier paper, I do not have the full text of Shattuck - so wrt Shattuck, I'm working on a combination of the parts of the paper that I've been able to find online, and various interviews with the author and/or discussions of the paper. (If it's legal for someone with access to send me a copy, I'd be delighted to see it; but I'm not willing to shell out $12 to obtain a copy through the journal directly just so that I can write a blog post.)

So - here's what I consider to be a few key differences between the studies:

1. Shattuck is very up-front about the limitations of his data. He's arguing that children that are currently classified as autistic by public school special education programs were formerly classified differently; a key part of that argument is based on the fact that until 1994, there was no uniform reporting of autism as a special education classification. In presenting his argument, Shattuck states: : "However, no reliable data exist that would indicate how the enrollment of children with autism was actually distributed among other enrollment categories before the 1990's." In other words, he admits that the data he's working with is incomplete - that some of the information that would be useful in supporting his analysis was never collected.
   
   In contrast, the Geiers use extremely poor data sources, but never own up to the weaknesses of that data. They present it as if it were unblemished, carefully gathered data.
   
   
2. Shattuck uses multiple analyses; the Geiers only used one simple linear regression. This is a big deal. When you use one analysis - particularly one simple analysis, you may find the appearance of a trend or correlation that is really an artifact of the analysis on that particular data. When you're working with real world data, you always try to perform multiple independent analyses to try to eliminate the possibility of false correlation. The Geiers do not do this.
   
   
3. Shattuck performs careful correlation analyses to show that his results are not the result of combinations of other diagnostic substitutions; that is, unlike the Geiers who find the data that supports their conclusion, and stop looking any further, Shattuck does the math to show that what he found is not the result of some other trend in the data.
   
   
4. Shattuck presents corroborative data from different sources to support his his hypothesis about the reporting rates of autism. His data has a known fundamental weakness: autism wasn't uniformly reported before 1994, so he shows statistical data to support the idea that autism was under-reported before it became a distinct required reporting category in 1994. The Geiers do not admit to any weaknesses in their data sources, much less show corroborative data to support their hypothesis where their data is weak.
   
   
5. Shattuck explains the trend behaviour of categorization data when new categories are introduced, showing how the autism data follows the standard trend, and demontsrating that the same trend occurs in other diagnoses after they became required categories.
   
   
6. Shattuck analyzes his data in a statistically valid way. He does not massage it, divide it, alter it, re-organize it: he treats it as a consistent data set over time, and analyzes it as such. The Geiers look at their data, and pick one arbitrary point to break their data into two independent data sets. That is absolutely not a mathematically valid thing to do. Shattuck is using math right; the Geiers are doing something that is unambiguously wrong.
   
   
7. Finally, Shattuck's work was reviewed and analyzed by another researcher, who points out some potential problems in his methodology; Shattuck admits to those weaknesses, but makes a reasonable argument for why the data he used is the best available.