I use Fedora 23 in a dual monitor configuration, my main monitor is 1366x768, my second is 1920x1080. When I start 0 AD, the full screen appears on my second, larger, monitor, but the size is wrong, as can be seen in the screenshot, and the mouse is detected to be in a location different from where it is, so it is not really playable.
I noticed that in the documentation for SDL_CreateWindow():
https://wiki.libsdl.org/SDL_CreateWindow
it says that if SDL_WINDOW_FULLSCREEN_DESKTOP is used, then the height/width parameters are ignored. I found that setting them to zero fixes the problem, although admittedly I do not have a deep undestanding of why.
My proposed patch is to set these to zero whenever full screen is used. This resolves the issue on my system by moving the full screen to the first monitor where it works normally.
An additional note, I found that alt-tabbing and then reselecting 0 AD is a workaround, and the window will appear on the first screen and work normally. It would seem to be good, though, if the user didn't have to figure this out. :D