If you are getting an error when visiting the Gnome Extensions Website such as: “You do not appear to have an up to date version of GNOME3. You won’t be able to install extensions from here. See the about page for more information.” in a red rectangle, and you don’t recall doing anything funky during your upgrade, then it could be due to a Firefox issue. I upgraded 4 of my machines to Ubuntu 12.10 and 2 of them gave me that error. I did find a workaround for now:
Open a terminal
Type Firefox -P
Select to create a new profile (I called mine alt)
Open Firefox with that new profile and visit the Gnome Extensions Website
You should be able to install your extensions from there now. I have to assume that there is some sort of miscommunication between my older profile for Firefox and the Gnome Shell Extensions website after the upgrade. Firefox moved to version 16 so perhaps this is somehow the reason why. Regardless, this is a decent workaround for now. If I find something more concrete, I will post it later.
Update — See the comment below which indicates that if you have “click to play” enabled in your about:config in Firefox, then it will cause this issue. Thanks for the contribution!