With Firefox Aurora, Mountain Lion hung - but the mouse still worked
Suspect an issue affecting the WindowServer process (brief edition for power users)

The symptoms you describe are familiar but not commonplace and in my case, not frequent. 

Diagnosis – at the time of the problem, if it recurs

Remotely, 

sudo sysdiagnose


After you regain local control, you can analyse the end result. 

Remotely, 

top -o state


Processes that are stuck should be at or near the top. 

Is WindowServer stuck for any length of time?

Workaround

If WindowServer is stuck, you might kill remotely – 

sudo killall WindowServer


– but this will cause a local log out, so be prepared to lose unsaved changes. 



This relatively short answer is tuned to the opening poster's confidence with remote ssh and bleeding edge stuff. 

For a more detailed answer, accepted under a similar question where the cause of a problem may be different: Suspect an issue affecting the WindowServer process (long edition)