[mikeash]

Another definition of "stability", perhaps more relevant here is: if you complete an orbit without crashing into the body you're orbiting, does that guarantee you won't crash into it later?

When orbiting a uniformly-dense sphere in an otherwise empty universe, this holds. When orbiting a body that approximates a uniform sphere in a universe where all other large bodies are relatively far away, this mostly holds. But significant deviations from a spherical shape can easily make most orbits unstable.

Little known fact: the Earth's Moon deviates enough from a uniform sphere to make long-term orbits tricky. Wikipedia article:

http://en.wikipedia.org/wiki/Lunar_orbit

Nice bit about a small satellite released by Apollo 16:

"Instead, something bizarre happened. The orbit of PFS-2 rapidly changed shape and distance from the Moon. In 2-1/2 weeks the satellite was swooping to within a hair-raising 6 miles (9.7 km) of the lunar surface at closest approach. As the orbit kept changing, PFS-2 backed off again, until it seemed to be a safe 30 miles away. But not for long: inexorably, the subsatellite's orbit carried it back toward the Moon. And on May 29, 1972—only 35 days and 425 orbits after its release"—PFS-2 crashed into the Lunar surface.

And this is all without any of the additional trickery coming from outgassing.

[wcoenen]

It's not so much the shape of the moon but the mass concentrations. The moon has significantly stronger gravity over impact basins. Based on shape alone (low plains) you'd expect lower gravity there.