Yeehaw, solved it.
Strange problem though, don't know how it was caused.
In UED, when selecting my "Screen0", it said "Screen properties (2 selected)".
When selecting my "ScreenSlideMap0", it said "ScreenSlideMap properties (2 selected).
Also when "Searching for actors" there was 2x Screen0 and 2x ScreenSlideMap0 in the list (two objects with the same name???)
Properties and location of both Screens and both ScreenSlideMaps were indentical.
It somehow copied itself to the exact same location (or maybe I did somehow).
In SinglePlayer this didn't seem to matter and it worked normally, however in Multiplayer the two got messed up.
It was not possible to select the one without selecting the other.
It looked like they are not possible to delete either.
After pressing Delete, they stay visible in UED and in the actorlist.
However, after saving/closing/opening/rebuilding the map they are gone.
I made a new one instead and now it works.
I checked the complete list to see if I could find more doubles, but there weren't any more.
I've seen this before with other objects (Movers, Pupaes), in the same map to be honest. It think it has something to do with copy & pasting.
Does anybody know how this is caused, so I don't make the same mistake again?