One of the biggest issues with the latest update to Firefox is that it sometimes does not always close properly.  While the browser closes physically, it does not close memory-wise.  Thus, it stays open in the background and still utilizes an obscene amount of system memory.  In some cases, this may even slow down your system to the point of having to restart.  You want to avoid your system crashing as much as possible in this case.

Restarting your computer will close Firefox, but it does not fix the underlying issue. In order to know if you have a problem with Firefox closing improperly, you want to close your browser and try to open it again right away. When you try to open it, a dialog box will pop up saying something about how Firefox is already running and you must close it first before opening another session. This means that it is running in the background still.

Now, to close Firefox, you must hit Alt + Control + Delete or open Windows Task Manager in another manner. Navigate to the Firefox entry in Processes and Terminate it. Once terminated, you will be able to open Firefox again normally. This will eliminate any issues you may be having; however, you may have to do this again until your next update. Mozilla is working on a patch, and for the most part, it does not occur in all downloads of the browser.

You want to ensure Firefox closes properly each time.  Otherwise, you may cause complications to the user profiles embedded in the browser.  This means that the next time you try and open it, you may not have your bookmarks and other preferences opened with it.  If you have recently updated Firefox and are having issues with it closing, follow the steps above to rectify it until the next update to the browser software.