Please state in which country your phrase tends to be used, what the phrase is, and what it should be.
Example:
In America, recently came across “back-petal”, instead of back-pedal. Also, still hearing “for all intensive purposes” instead of “for all intents and purposes”.
“Hold down the fort” and “the proof is in the pudding” is how those phrases are currently used in the US, regardless of their origins, and they still make sense. “Could care less” is objectively wrong unless you’re trying to indicate that you do kinda care.
The last correction is accurate.
Sometimes I like to be extra specific about how it is physically impossible for anyone to care less than I do about <something>.