Actually, "I could care less" is a transplanted idiom (from Yiddish), and is correct. It implies "... but that would be too much work." It is an Americanism, though, and is not generally understood outside of the lingering cultural influences of the "borscht belt".
English -- any natural language that's progressed beyond early creole, for that matter -- is not, and should not be treated like, a completely self-consistent system of formal logic. "Me" (or other "object" pronouns) in a compound subject is correct, as are double negatives, split infinitives (English doesn't actually have an infinitive, it has a form of phrase that occupies the function of one), and so forth. The prescriptivist dictates of Lowth, Murray and Cobbett are an artificial imposition on language that rejects them at every turn. It's time to use the real grammar of the language, rather than trying to structure English on some formal (and, it would seem, rarely spoken) version of Latin or Greek.
English -- any natural language that's progressed beyond early creole, for that matter -- is not, and should not be treated like, a completely self-consistent system of formal logic. "Me" (or other "object" pronouns) in a compound subject is correct, as are double negatives, split infinitives (English doesn't actually have an infinitive, it has a form of phrase that occupies the function of one), and so forth. The prescriptivist dictates of Lowth, Murray and Cobbett are an artificial imposition on language that rejects them at every turn. It's time to use the real grammar of the language, rather than trying to structure English on some formal (and, it would seem, rarely spoken) version of Latin or Greek.