"Romney and Clinton came of age during a time of an active military draft; both used a completely legal military deferment to purposefully avoid military service. ... Obama came of age in a time of no active draft, thus he was free to choose – he chose public service versus a military career, but did not employ any tactic to purposefully avoid military service."
Though similar, purposely and purposefully are not entirely synonymous. The distinction is worth preserving, I think. (Full disclosure compels the admission that my opinion in these matters is not always highly regarded. Some people seem purposefully indifferent.)
Purposely means "on purpose; deliberately," and in the newspaper item above, I think that's what was intended. Clinton and Romney deliberately avoided military service. Obama didn't have to.
Purposefully means "with conscious purpose; in a highly deliberate manner": "Pryor purposefully strode across the chamber to confront McConnell."
Purposely used to be more common, but for some reason, purposefully has gained in popularity. I see it frequently where purposely would be a better fit.
A similar thing is happening with single and singular. Singular once was used almost exclusively to mean "exceptional; odd," while single meant "sole; individual." Now singular seems to be crowding single out: "Ask Attorney General Dustin McDaniel about extra money. The other day he announced the state's part of another big national legal settlement. Then he presumed, as ever, to decide singularly where those millions will go." McDaniel's decision may have been an odd one, but I think the writer meant that he acted alone.
"Both the secretary of state and the attorney for the amendment's sponsors told the court that it all came down to how detailed of a look the office should take when it performs a prima facie review of submitted signatures." The unnecessary of is a kind of down-home way of expressing oneself. How detailed a look would be sufficient. Still, the way the Razorbacks' season is going, I expect we'll be hearing How bad of a loss was it quite a lot. These are the times that try men's usage.