I really love Firefox, but was looking for way to disable the private browsing for one of my clients. I found a few work arounds but this appears to be the best option out there. It is just an addon, but can only be disabled when in Safe Mode. This extension is only a simple fix. A technical savvy user will still be able to start Private Browsing.
What it does
This addon disables the Private Browsing menu option and keyboard shortcut. Since version 1.4 clearing the browsing history is also disabled. A side effect is that bookmarks can no longer be removed unless in Safe Mode. (You can still move them to a folder that you can name “Remove”.)
If you need to remove this addon, boot into safe mode and go to remove addons.