Results for Knott County KY are probably backwards

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The biggest was a 40-point swing to McCain in Coal County, Oklahoma.

There are only about fifty people employed in mining in Coal County.

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Wow, Coal County even voted for Mondale.

Why should there be surprise that an utterly working class area voted for Mondale?

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So, it's an agricultural processing county mostly?  What's up with that?

Presumably it used to be a mining area. There's a town in the county called Coalgate. Perhaps there was a Mr Coal, but it is, just about, on the main Oklahoma coalfield. Mining communities do often last longer than large scale mining; it's been decades since there's been much mining in the Scranton/Wilkes-Barre area, say.

More important is the fact that it's in Little Dixie.

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Eastern Kentucky was pretty close  to [but not on] the epicenter of the insane anti-Obama shift of Appalachia.  Look at Arkansas, for example, at its entire state-wide swing despite a 10% swing to the Democrats. 

No part of Arkansas is in Appalachia.