I know you're using OS 10, however there is very little on this subject anywhere and I FINALLY found a two-part solution for this under Windows XP. You might try this link, otherwise I hope others may find this to help them in XP. This little trick also removed the "Clear Recent History" button as well :)

http://kb.mozillazine.org/User:Dickvl/Private_Browsing_disable

It looks super complicated, but in reality it was ridiculously easy. The only part I followed was under "Extension code for pbdisable". You just follow the simple steps of copying that big clock of data, paste it in your browser/URL bar, save it, change the name, then drag it into any open Firefox windows, restart firefox, you're done. Took me all of 25 seconds!

Also, something else that I did which is probably overkill, but run a search on your machine for a file called "nsPrivateBrowsingService.js". Simply delete it! Now, even if someone disables the plugin that that removes the Private Browsing button, then this way the program can't run at all no matter what. Just be sure to dump your recycle bin when you're done.

I'm afraid it does not make sense to disable the private browsing mode, because the user can clear the private data at any time using the Tools -> Clear recent history... menu item.

You can set up your router or a firewall, or look for some website-blocking addons at http://addons.mozilla.org instead.

On OS X you can't use code in userChrome.css to modify the menu bar.
The menu bar is maintained by the OS on a Mac and not by Firefox.

I advise not to remove the file nsPrivateBrowsingService.js
That file is a browser component and other components may rely on its present and removing that file can have impact on the functioning of Firefox.

Gryllida -you can track usage with the antiporn extension and add-on extensions can be locked down with the public fox extension but private browsing subverts them as well as others. Using a firewall works great at one location but not for a laptop that is mobile. the link mentioned in bmag360's post works on firefox4 but not 5. I work for a digital school that gives each student a laptop to use and we need to lock down this feature so we can give students a relatively safe browsing experience and help to keep parents and teachers informed of any dangerous/in-appropriate internet activity.