How can I verify that pop-up upgrades are safe?

hello robfeimer, first you're right to be careful about such notices, since recently it has become a fairly often used tactic by malicious websites to try to trick users into downloading malware-infested versions of the browser. as a rule of thumb, when you are getting prompted to download and run a .exe file to update firefox, it will be a scam, since firefox handles updates internally...

you can always initiate a check for updates manually in the firefox menu > help (?) > about firefox.

Any time you want or need to check for upgrades, go to the web site of the True Owner of the program in question. For example, to check out Firefox, go to Mozilla.org. {web link}