When I open multiple Finder windows in Mountain Lion, I find that, no matter what virtual desktop I go to in Spaces, all the Finder windows remain where they are. However, when I open, say, Skype, for example, the window only stays in one of my virtual desktops, as expected. When I 4 finger swipe to another Space, the Skype window disappears. Why doesn't Finder do this? It's really bugging me.
You just need to ctrl + click on the Finder Icon in the Dock. Go to the Options, and choose how the finder windows show in Desktops
All Window show in Desktop Spaces
All Window show Only in the current Desktop Space. When your are in another desktop space it will jump to the one for finder when you open folders into windows or switch to the finder.
Each finder windows will stick to the desktop space you open them in.