Not really. The switches just won't stop even when there's a map their not suposed to be on.
In that sense you can say that switches are global.
It doesn't really matter where you go.
Let's say you turn a switch on. This switch will keep being turned on until you turn it off.
I'm not really sure what your problem is, but you can try this:
In the editor: Look through your game and see where you are using switch operations in the events.
Play the game. You can look on the values of your switches when pressing
F9 (might be F8 or F10, can't remember).
Note that you can't look on any local switch using that feature.
If you see a switch not behaving like it should (ie. being off when it should be on) you know in which event the problem might be.