My version of the "could care less" pet peeve (which is annoying but tolerable) is when people reverse the order of the cases in a "let alone" phrase. The entire point of "let alone" is that you fail to meet the general case, so of course you don't satisfy the specific case.

For example, if I asked someone "Have you ever been to Germany?" they might answer "I've never been to Germany, let alone Europe!" As is, this is nonsensical, but if you reverse the order, all is well. Most examples in the wild aren't this obvious, but they're commonplace once you start looking for them.