In going through our usage guides, we occasionally come across linguistic jokes – not terribly funny, admittedly, but they apparently appeal to writers on usage. And they have done so from the earliest days of the usage guide tradition onwards, so they may be said to be part of the genre. We once conducted a poll to see whether modern readers still appreciate the jokes found in Five Hundred Mistakes of Daily Occurrence (1856). Few people took the poll, so perhaps they no longer do (you may want to find out for yourself if you have a moment to spare).
Here is a more recent one, which I just found in Webster’s Dictionary of English Usage (1989):

Frank Vizetelly
feel bad, feel badly It is a standard joke of usage writers to remark that someone who says “I feel badly” must be complaining about a defective sense of touch, or thick gloves, or numb fingers. The Joe Miller who invented this hoary witticism may have been Frank Vizetelly, whose 1906 A Desk-Book of Errors in English has this: “However, feel badly is correct when the intention is to say that one’s power of touch is defective…” Subsequently joining the merry band of misunderstanders we find Bierce 1909, Evans 1961, Harper 1975, 1985, Freeman 1983, Kilpatrick 1984, and others. Of course, they know and we know that people who say “I feel badly” simply mean they feel bad.
I do wonder whether such jokes are effective ways of explaining readers what is wrong with a particular construction, here the use of bad as a flat adverb.
Bad isn’t a flat adverb in feel bad. It’s a predicate adjective.