Wow. We found Luna in our woodpile in May when she was maybe 6 weeks old, and she already knew how to use the litter box.
I've only had "accidents" when the cats were in heat (or they are male and hitting puberty), or when they're really angry at me for some reason (like going away for the weekend or bringing in a new animal into the house).
I just wish the older cats would teach the kitten that it's NOT OK to jump up on the plant shelves and knock flowerpots over.