One point that strikes me is that they seem to be implying that the genetics are directly responsible for worse health, whereas all they have shown is a correlation between a few random factors and some numbers on an intelligence test.

They are relying on other studies that show a correlation between health and intelligence to conclude that people with genetic factors have worse intelligence and hence worse health. But we don't know if poor health leads to poor intelligence or vice versa (or neither), so their chain of causation may not even exist. Likewise, those studies presumably applied to the general population; maybe people with club feet are an exception?

Also note that the researchers gave the subjects a number of physical tests in addition to asking about the genetic factors, but they only chose to report on the correlation in mental tests; if you are trying to show a correlation between genetic factors and general health, why not use the health tests directly and not need to argue via intelligence? If it turns out that the mental tests were correlated to the factors, but the physical tests weren't, then they have actually found a group of people for which intelligence and health is not correlated, which actually disproves their theory.

Arden explained that while she and her team agreed that factors such as poverty and looking after one's health also make a difference to health, this study, which the authors describe as a "proof of concept", shows there could also be a genetic factor which warrants further investigation.

For the sake of argument, let's assume that poor intelligence causes poor health. It's entirely possible that the subjects' genetic factors had zero direct influence on their intelligence, but the fact that they grew up "funny-looking" caused them to have less income or to perform poorly in school, which indirectly caused the lack of intelligence. This means the problem could be corrected entirely by devoting more resources to learning or by having the subjects undergo cosmetic surgery -- a big hole in the researchers' theory of a "genetic fitness factor" that is somehow causing both externally visible defects as well as internal health problems.

Edit: And this:

The researchers then compiled an index of physical health by aggregating "abnormality counts" in 8 categories and by using a statistical tool called regression analysis they were able to show that intelligence was a signficant positive predictor of 6 of the 8 categories.

Why would they aggregate counts into categories? Perhaps because none of the individual abnormalities correlated strongly enough with the intelligence tests? (Everyone knows you can redistrict an evenly divided state to favor a particular party...)

Never mind that some of these abnormalities are conditional on lifestyle, which is already correlated with intelligence. (Who is more likely to discover they are slightly predisposed to a hernia -- a college professor or a dock worker? A kid who got beat up a lot is more likely to have a malformed nose -- is he more or less likely to have a quality education?)

And it would be pretty funny if those other two categories were significant negative predictors -- e.g. people with club feet turned out to be more intelligent than the general population and hence healthier.

And, of course, the sample population is heavily biased: They're all Vietnam-era vets. The study leaves out everyone whose malformities were too great for them to serve as well as everyone who was smart or well-placed enough to get out of the draft.

(This may all be addressed in the paper, but I'm not paying $30 to find out.)