Several times now I’ve had one desktop get into a mode where you cannot click on anything. You can use the keyboard to navigate between apps and everything seems to work normally, except mouse clicks. At first I suspected my wireless mouse, but after trying a few alternative mice, I ruled that out. The first time it occurred after a wake from screensaver, so I suspected that was the issue and just restarted. Today it happened while using Safari, so I investigated a bit further.
I found this in the log file:
May 14 10:57:44  Warning: Program "UniversalAccessApp" posted a mouse-down, blocking hardware events, b
ut did no further mouse activity
And as suspected, killing Universal Access (ps auxw|grep Universal, etc.) brought back mouse clicks. At this point I do not know why UniversalAccess decided to send a mouse-down, or what I have enabled on this workstation that is not on my laptop or home system, but just in case anyone else gets stuck in the same situation, there is a way to regain control.