I think that one is an American idiom, so it's not exactly the same class as other grammatical errors. Most Americans know what it really means. Even people who have otherwise perfect grammar might occasionally use it. Using this expression accentuates the idea of how little you care because you are not even caring enough to have perfect grammar. So it is a little bit clever in that way and sort of likable that it is a peculiarly American expression.
I could/couldn’t care less. Either way to say it is correct. They mean slightly different things.