...as in the phrase, “comes back like a bad penny.” Where does the “bad penny” come from?

A bad penny is a false or snide coin and there a numerous cites to them being common, and in the nineteenth century ‘causing misery’ presumably because people accepted them in good faith and then couldn’t spend them - a big problem if you were poor to start with. The earliest cite for someone being compared to one is from the 14th century ‘lettered men are likened to a bad penny’ The earliest cite in OED to ‘coming back like a bad penny’ is 1937, they don’t suggest why but I suppose they were an unwanted nuisance that were hard to avoid.

I’ve always heard it as “A bad penny always turns up”.  Googling led me to:
http://www.phrases.org.uk/bulletin_board/26/messages/257.html
which further googling found:
http://www.gutenberg.org/dirs/etext01/redg10.txt
Sir Walter Scott’s “Redgauntlet” written in 1823-24 which contains the line:
“Bring back Darsie?  little doubt of that--the bad shilling is sure enough to come back again.”