I wonder how that would have effected migration of humans across the planet, and how their various cultures adapted and formed. Some would see the Moon every day and night, others might only see part of the moon on the horizon. Others might only have distant stories of ancestors who saw the Moon and left it, or stories of the Moon leaving them. Others might forget about it entirely...

I imagine some cultures might resist moving away from where they could see the Moon. The omnipresent Moon might become a sort of god to those that lived under it, such that they would fear traveling so far away from it that it left. Maybe others would fear the perpetually darker nights.

This seems like it could be the premise of a science fiction story, perhaps similar to Asimov's Nightfall.

It would certainly be trivial to make a diagram of el/az of certain craters or mountain peaks referenced to earth magnetic north so as to make chronometers and such for determining longitude irrelevant. No need for precision chronometers would have some subsequent effects on the industrial revolution etc. Of course on the other side of the planet they'd need such "high tech" instruments as chronometers so in sci fi mode, the high tech far siders would likely end up conquering the near siders via higher technology.

A geostationary moon, if tidally locked to present the same face to the earth all the time, would certainly be a convenient termination point for a space elevator. So rather than a space elevator dumping you off in space, you'd be dropped off on the moon. Of course some genius will start transferring the earth's biosphere, oxygen, carbon, etc to the moon and just dumping it there to terraform it. Obviously (?) you can't just run a garden hose to the moon and suck on the moon end and expect a flow rate, although it is sci-fi so maybe if you pressurized the earth side up to something approximately ridiculous, you'd be able to squirt water across to the geosync moon. I would not want to be in charge of that project...

_Encounter_with_Tiber_ by Aldrin and Barnes used such a premise, except the habitable alien world was a tidally locked moon around a gas giant.

More likely, and perhaps even more fun, would be a moon that was almost in geosynchronous orbit. What would be the effect on civilization and the biosphere if instead of 1 meter tides with a 12 hr period we had 100 meter tides with a 100 year period?

That is a really interesting problem to calculate. What would that water mountain look like? Could you even tell?

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The area of deflection would likely be very large and gravity would still be normal to the surface of the water, so no, you probably wouldn't be able to tell. You might perhaps notice the horizon being closer.

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In orbit only the center of mass of the object is in free fall.

Anything farther away is falling "up" and anything closer is falling "down". So the water would fall "down" (i.e. toward the moon).

But since there is plenty of gravity on earth this would mean the water is effectively just lighter. And water on the other side of the Earth is heaver, and would flow to the lighter area until the lighter side was tall enough (i.e. had enough extra water) to balance that out.

Since the position is static the earth itself would deform too eventually. So I believe the answer is "not much".

So the earth would take the shape of of an egg and the ocean would ride over it with a constant depth?

I wonder how that would effect rocket launches? Would it be better to launch on the far side of earth or the moon side?