Node Add / Edit Options Vertical Tab Problem
Here is a series of things I would try. Check tabs after each test.


Try with a different browser.
Flush all caches (that one often solves a lot of problems).
Put your site in maintenance mode and Run updates (update.php).
Disable the Overlay module.
Disable all modules. Flush all caches. Re-enable all modules.
Update to the latest version of core if you can (currently 7.22).


Number 5 is a bit time consuming but it has solved issues for me in the past. First, make a list of all enabled modules. I do this with screen captures. Second, start disabling modules (except maybe Admin menu). You won't be able to disable all modules at once. It may take half a dozen Save configuration to completely disable all modules. When done, Flush all caches and while you're at it, clear your browser's cache too. Finally, re-enable all required modules. Run updates. Run cron. Flush all caches.

Hope this helps.