On one of my Joomla 3.2.1 sites, when I activate JCE the save and Cancel buttons don't work in the Article manager. I have no other extensions installed. With no WYSIWYG or a different one it works. I can give you access to the Admin if you want it.
It seems that module parameters haven't been configured properly. Please make sure that you are using a valid twitter username, and
that you have inserted the correct keys. Detailed instructions are written in the module settings page.