Update: I was reminded that using visibility: collapse for menu items leaves them in the key navigation. Instead, you should use hidden="true" or in places that doesn't work (context menus) display: none.
In my previous post, I showed how to setup a basic extension in Firefox. Having this extension will allow us to do some Firefox customization. Before I get into this post, though, I wanted to clarify one thing. I had you put your XUL overlay in the root directory and point your content directory to ./. I did that to make things simpler but in practice you'll want to separate your files. The structure most commonly used is a chrome directory with a content subdirectory underneath. In that case, the directory in the chrome manifest would be chrome/content/.
With that out of the way, let's customize Firefox. We're going to prevent a user from accessing private browsing. We need a disclaimer here, though. We are not removing private browsing, we are just removing access. So if the user has an add-on that invokes private browsing, or if they have access to about:config, they can still turn on private browsing. For any of these customizations, there's an expectation that the right things have been done to prevent the user from accessing functionality via other means.