You have a recent version of Firefox and you run into a page that requires a QuickTime plug-in.
It asks you to install the plug-in manually but there is no way to do it. You probably looked for it everywhere and even Apple web site says, "it comes with your Mac already."
It appears that if you have a QuickTime plug in file in /Library/Internet Plug Ins/QuickTime Plugin.plugin this issue can occur. It also appears that this isn't really needed.
I had this Mac for quite a while with all different versions of Firefox running, so I would not be surprised if the old plug-in was not removed when it had to be after a certain version of Firefox.
If you hesitate to do any of these "internal" activities below, then try using Safari browser. That's I have been getting around before I found this answer.
- Quit Firefox
- Open your Finder and head to /Library/Internet Plug Ins/ and cut QuickTime Plugin.plugin and paste that onto the Desktop or any other directory outside of it. In fact you will need this since Safari will need this.
- Start Firefox again.
- Try the page with Quick Time again