This Politico story says that the reason Mitt Romney didn’t challenge Rick Santorum’s presidential primary petitions in Illinois is that if he had, then Santorum would have challenged the Romney petitions.
Romney’s petitions might have been invalid because Romney’s statement of candidacy was not notarized by an Illinois notary, but by a Massachusetts notary. The Politico story, at the end, says that the location of where the notarization was done is not relevant, but does not get into the issue of whether a notary only recognized by Massachusetts is free to notarize Illinois election forms. Thanks to Rick Hasen for the link.