This morning, my Firefox started acting up. It would freeze when I attempt to upload a file or use the right-click Save As… functionality. Upon a closer look, however, it turned out it wasn’t really freezing, but taking a very long pause; eventually, the File Upload or Save As… (as the case may be) dialog would be displayed.
It turns out that the reason for this behavior is that I recently downloaded to (or uploaded from) a location that is no longer accessible. In my case, it was a folder on a network share, but I would guess something like this could also happen with a removable storage device, such as an external hard drive or a Flash drive. So Firefox was essentially trying to access the location it accessed before, taking its time to repeatedly try it and eventually failing.
Now that I understood what the problem really was, fixing it was a matter of seconds. I typed about:config into the Firefox address bar, scrolled down to browser.download.lastDir configuration variable (highlighted in the picture below), and changed it from its old value (which was something like \\myServer\myFolder) to C:\temp, which was a name of a directory that exists on my system.