Ok, hang on a sec.
Regarding the straw man, the study itself states: "At this point of our analysis, the cause appears to originate with electronic voting equipment; the problem does not exist when manual methods are used." But the Iowa example shown two pages later flatly contradicts this. See p.5 and p.7: Linked Study
Regarding Iowa: "GOP officials discovered inaccuracies in 131 precincts"... Perhaps, but the scope of these inaccuracies were magnitudes different than the purported "vote-flipping" implied by the study. Romney lost less than 50 votes on the statewide recount (relative to Santorum), compared with the study's implied 7850-vote gap. Data from the missing eight precincts couldn't come remotely close to closing this gap. So even correcting for the found inaccuracies, we're left with over 99% of the purported discrepancy unaccounted for. Were the fraudsters simply 99% successful at covering their tracks? If so, wouldn't there be many fewer precincts with discrepancies? The ~50 vote recount correction could easily be due to random human error.
Regarding cherry-picking: there is no question that there is a bulletproof correlation between precinct size and vote ratios, in Iowa in this primary. (The null hypothesis has been proven false, in other words.) The real question is whether that correlation ITSELF correlates strongly with the type of balloting/counting used, and for this there are very few data points shown. Are there counterexamples (places where electronic voting was used but the anomaly is not seen, or vice versa)? How many? What distinguishes the ballot-counting process in the Iowa Caucuses from, say, FL Palm Beach County (where there was no anomaly observed)? What were the correlations, if any, in all these different states and counties, of precinct size vs a priori voter registration (Republican / Democrat ratio)?
Can anything be gleaned from this?
Again, it would be nice to see the study peer-reviewed, and to have stronger logic why the correlations COULDN'T be a result of "natural causes", rather than just we can't think of a way. (I agree that there is no other immediately obvious explanation, but that doesn't mean one doesn't exist.)