Is there a command line switch for firefox.exe or an "about:" URL that will either force an update check or at least display the Help/About dialog, which checks for updates and tells if you're running the latest version?
One site claimed that the "about:" URL was the same as menu Help -> About, but it's not.
I built a program to automate the updating of various programs on my machine, and most programs have command line tools for checking for updates. Windows update has wuauclt.exe, Java has jucheck.exe. For some applications, I can even automate the interface, but it's difficult in Firefox, because the main window title is unpredictable (it depends on which web page is active), and all Firefox windows seem to use the exact same window class name.
Best Answer
The trick is to download the partial update (.MAR) file and running the updater via the command line.
Check the detailed article Software Update:Manually Installing a MAR file at MozillaWiki. It explains the sources to acquire the MAR files from, which is something you may want to automate as well, as the links are fairly well structured/canonicalized), as well as the steps to execute the installer.