I was guessing that it could not be controlled from earth because of the time delay for signals.
It all depends on what you're doing, because the delay is just a minor nuisance for some things and an insurmountable obstacle to others.
Today we have some pretty sophisticated spacecraft computers. They are absolutely indispensable for spacecraft in the outer solar system conducting time-critical flybys (e.g., the Voyager missions to the gas and ice giants). Well in advance of each encounter you upload software to the onboard computer to tell it what observations to make and when. The software also handles as many faults as it can. Some are simple; if the primary star tracker fails, just switch to the backup. But it's impossible to anticipate
every possible failure, so for many the computer typically puts the spacecraft into "safe mode", a stable configuration that avoids further damage, establishes a minimal communications link to earth, and waits for further instructions. This obviously takes time, but it gives the humans back in Mission Control an opportunity to analyze the problem and devise a solution.
There's a good analogy to the vertebrate central nervous system. The brain is like Mission Control; it can make the most complex decisions but it's slow. You don't want to take the time to ask your brain what to do when you touch a hot stove; you'll have a badly burned hand before you get an answer. That's why we've evolved a spinal cord reflex that causes you to jerk your hand away from a hot stove without even thinking about it. The onboard computer on a spacecraft implements its "reflexes".
The big problem comes when you need to handle situations more complex than the onboard computer can handle, but you don't have time to consult with Earth. In this case you really have no choice but to fly a trained crew. The Apollo LM didn't have sensors and onboard computers powerful enough to spot and avoid obstacles and land entirely automatically, and the time lag for remote control from earth would have been unacceptably long. It simply couldn't land without a crew at the controls.
There are also interesting ideas to land robots on Mars controlled by astronauts who stay in Martian orbit, thus keeping the delays low without having to figure out how to return those astronauts all the way from the surface.
I found the gravity anomalies (if that is the right word ) to be fascinating, is the cause understood?
Sure. No planet or moon has a totally uniform internal mass distribution that can be modeled as a single mass at the center. None are perfectly spherical either.
The moon's gravity field is much lumpier than the earth's mainly because it's so much smaller. It's tidally locked with earth, so we never see the lunar far side. From earth we can track a satellite in lunar orbit whenever it's on the near side, and we can accurately infer the lunar gravity field from that tracking data. But you can't track a lunar spacecraft behind the moon, and that has kept our gravity models for the lunar farside much less accurate than those for the near side. And you need the gravity of
both sides to accurately predict the motion of a satellite orbiting the moon.
This problem has attracted quite a bit of attention in recent years. The Japanese Kaguya spacecraft had a subsatellite in a separate lunar orbit to relay tracking signals between earth and the mother ship when the latter is behind the moon, and that substantially improved our lunar farside gravity models. But the real improvements are coming now from the two US GRAIL spacecraft where each can track the other with extremely high precision, store the data onboard and dump it to earth when they're above the lunar nearside.
