Yes - well, my problem was that I couldn't set it up to allow for VNC since the screen was messed up - but when trying - and failing - to connect to it through VNC, it suddenly worked again. I don't feel that this helps me understand the problem and when this happens again, what to do. But it works for now, and now I've set it up to allow for VNC access. I will accept your comment as a solution to my immediate problem and post a new topic should it occur again.

By the way, no monitor is attached to this server

Works for me, for the moment :)

The problem is that the Screen Sharing (SS) client is not getting a clear indication of what screen resolution the Server is running at (it doesn't matter that there is no physical screen attached to the server).
On your garbled screen you can see it is trying to display the desktop but it appears as if everything is split into slices and distorted.

Restarting the Screen Sharing/ Remote Desktop service on the server sometimes resolves it .. or restarting the SS client (which is not a brilliant application in any case)
I prefer COTVNC and JollysFastVNC for speed and stability.

All of that would make sense if the login screen wasn't shown perfect. I can login and logout several times and when logged in, it's garbled, when logged out, it's not. It's never the other way around and it's always that way. I think it's weird, regardless.

Screen resolution is set on a per user basis .. so the resolution set on the login screen is OFTEN different from the screen resolution selected by a specific login user.

Until you login .. the screen resolution settings are not changed and are probably at a default setting e.g. 800x600 but once you login the settings may be 1024x768.