Since Pluto's demotion, I've believed there should be some limitations on what could be considered a moon.
Otherwise, like Metryq said, every rock bigger than a baseball in Saturn's rings could be called a moon.
"Every rock bigger than a baseball in Saturn's rings" wouldn't show up as a distinct object in a telescope, though, and therefore wouldn't be identified and named and wouldn't be considered a moon.
It's sorta like the definition of "Island." The cutoff seems to be mostly arbitrary, but a good rule of thumb is that if it's too small to be labeled on a map, it's probably not really an island.
Significantly, Jupiter has something like 60 moons, but astronomers -- and anyone else, for that matter -- only really care about the four major ones, the rest are just puny little asteroids zipping about in random orbits.