You can do this:

• Download a new copy of the Firefox program: http://www.mozilla.com/firefox/all.html
• Trash the current Firefox application to do a clean (re)install.
• Install the new version that you have downloaded.

Your profile data is stored elsewhere in the Firefox Profile Folder, so you won't lose your bookmarks and other personal data.

That sounds like what is described elsewhere as the "last resort," and it seems as if it almost entirely defeats the purpose of updates.

Other Mac software can be updated from any account:

• If the currently logged in account is an administrator's account, the updater asks for password confirmation.
• If the currently logged in account is not an administrator's account, the updater asks for an administrator's login and password.

In either case, after that authentication, the update just works. Why can't Firefox do this?

Then you need to check and repair the disk permissions to make sure that you have write access to all files. If something went wrong a previous time and some security permissions got mixed up then it is usually much quicker to delete everything and start over and hope that it goes well this time (i.e. you won't have to do this with the next update) then try to find out what exactly is wrong.

If I can't update because I don't "have write access to all files" I'm not going to be able to delete them either, right?

Last I knew, once authenticated as administrator I am effectively root, which should mean that I have write permission to the entire system. Trouble is, it is not even asking me to do that authentication. How do I make it do that?

You should have write access as administrator and be able to delete the files, but programs may not have that permission.

Then they are supposed to ask me to authenticate, as I described on October 23, right? Again, how do I get Firefox to do this? What could be stopping it?