I have 3 installations of the same site (dev, staging, production). Apart from some front-end and content differences they all use the same plugins and the same settings yet for some reason the floating toolbar and content field disappears in Firefox, but only on the prod site. I haven’t installed anything or changed any settings on the prod site recently.
I should have been more specific. In the Manager in the upper-right corner, the row of buttons (Save, Duplicate, Delete, View etc.). Menubar is probably the correct term.
I’m currently out but will look into the browser errors when I can and report back.
Have you tried deleting all the files in the core/cache directory and viewing the site in private or incognito mode. Sometimes the kind of problems you describe are caused by an outdated cache file or cookie.