Can there be such a thing as a totally complete job description?

Answer 1

yes - because the phrase "any other responsibilities as may seem fit" or simmilar is usually added.

Answer 2

Of course there is. It's called "other duties as assigned." If you're really lucky, it says "other related duties as assigned." As a manager at an aquatic center, I always wished it said that because my bosses would want to make my lifeguards do manual labor instead of watch the water!