Recently, (since installing OS X Yosemite,) I am occasionally unable to use the two-finger swipe gesture to navigate between open full-screen spaces on my Mac. They keyboard shortcuts will also stop working. Alt-Tab does not allow me to switch to the full-screen apps. It appears to be a full-screen issue, not an actual mouse or keyboard issue.
I Googled, but nobody seems to have a solution other than restarting the Mac (which does work temporarily.) The issue popped up today, and I started closing apps in order to make sure the restart wouldn’t cause me to lose any work. After closing the Calendar app, gestures began working again. Keyboard shortcuts start working again, as well. I was suddenly able to switch between full-screen apps.
I have no idea if this will help everyone, but give it a try. If you are suddenly unable to switch between spaces in OS X Yosemite, close the Calendar app and see if that solves the problem.