Firefox 26.0 always says it is out of date and that it is up to date
When Firefox starts the first tab is "You're almost there!" saying the version is out of date, but the Help > About > window shows Firefox 26.0. I have a screen shot if you want it. If I click on "get the newest version" I get "Congrats! you're using the latest....."
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You can check for problems with preferences.
Note that your System Details List shows that you have a user.js file in the profile folder to initialize some prefs on each start of Firefox.
The user.js file is only present if you or other software has created it, so normally it wouldn't be there. you can check its content with a plain text editor if you didn't create this file yourself.
The user.js file is read each time you start Firefox and initializes preferences to the value specified in this file, so preferences set via user.js can only be changed temporarily for the current session.
Rename or delete the prefs.js file and possible numbered prefs-##.js and user.js files to reset all prefs to the default value.