Everyone (well, OK, not everyone, but most people interested in this kind of stuff) is familiar with "mascons" (mass concentrations) on the moon, that cause perturbations and instability in the orbits of objects around it. Interestingly, though, the earth's gravitational field isn't all that symmetric, either, based on results from the GRACE satellites. I think that it's kind of amazing how sensitive these detectors are:

The concept is simple. The two satellites, each about three metres long, follow each other in identical orbits roughly 400 kilometres above the Earth and 210 kilometres apart. Microwave instruments measure the distance between them, precisely enough to detect variations smaller than one percent of the width of a human hair.

"[It's as though] you have two automobile-sized things, one in Los Angeles and one in San Diego, and you're measuring the distance between them to the size of a red blood cell," says Watkins.

As one satellite and then the other passes through wrinkles in the Earth's gravity field, they speed up or slow down slightly, shifting the distance between them. By measuring these tiny yo-yos, scientists can calculate the gravity field that produced them, mapping the entire Earth about once a month.

But the dispersions are much smaller, relative to the size of the body, so it doesn't create the same levels of perturbations that can result in instability. Pretty cool graphic.

Back in 1960-62 when I was going through MIT's Aero and Astro program, the consideration of mascons on Earth was quite common with the understanding that position errors of up to about a quarter of a mile were possible due to deviations of the local vertical around mascons. They alluded to geographic surveys that were used to evaluate guidance error inputs for ballistic missiles, notably submarine-launched missiles or air-launched missiles like Skybolt. It will be interesting to see whether the mascons are stationary, or whether they move around.

I remember reading that during or shortly after Apollo there was a proposal for a Lunar Orbiting Space Station, dubbed LOSS. But past a point they realized that lunar mascons would perturb the orbit to the point where eventually the low parts of the orbit would be below the tops of mountains. Then someone couldn't be restrained from saying, "LOSS would have been a true loss".

But a station at L-1 would provide fine access to the moon.

You know looking at that map the areas of high gravity seem to correlate with highly religious regions. Whether the presence of God is collecting energies or the higher energies are making people all the crazier remains to be seen.