My worry is that networks can be established on and orbiting the moon which become extremely difficult to get data from if someone decides to abuse it.

You can raid a data center if bad actors are utilizing it to break the law, but if some billionaire is using a moon relay to do bad stuff, the best you can do is de-allocate their bandwidth on the spectrum since you can't just hop over to the moon. Or to some craft in space. De-allocation would depend on international cooperation, inevitably. It would suddenly be far, far easier to break the law on networks and become effectively untraceable. This equipment will certainly be privately owned (like the prototypical versions already are) and it will be an extremely potent tool for breaking the law without consequence.

Also it looks like allocation of spectrum doesn't mandate logging, so you could in theory have data centers floating around which don't even trace who did what and how. If any country chooses to facilitate this and allows this communication to be received, and propagates it to their internet, what does the rest of the world do? Is it cause for conflict? Are there ways to stop the traffic from outside of the country?

I'm sure I'm missing tons of pertinent details here and this isn't meant as a totally impenetrable statement about the future. It's more so that I have concerns that this could actually happen based on the limited understanding I have. So feel free to tear it apart and let me know how dumb my idea is.