Can't upgrade from Firefox 3.5.3 to 3.6.x in OS X 10.5.8.
I've downloaded the latest version of Firefox, quit and restarted and I still end up with my older version of Firefox.
Download a new copy of the Firefox program: http://www.mozilla.com/firefox/all.html
Trash the current Firefox application to do a clean reinstall.
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.