I recently upgraded to 12.04 and am running Gnome-shell. I use both FF and Chrome, but rely on Chrome for use with Google apps. In the last couple of months with recurring frequency I lose my ability to navigate open tabs especially when the browser if full screen. If I open a new tab, I'm often able to recover my ability to navigate, or if I resize the browser so that it's not full screen, I can navigate again too.
I'd experimented with using Chromium, and eventually experience the same behavior.
This may not be related, but I also often lose my ability to drag and drop files/images into Gmail.
Thinking that this might be extension related, I have disabled all extensions, and experience the same behavior.
Very frustrating, as mostly love Chrome.