If you get a pop-up message asking to update Firefox or plugins or scanning for malware then such a message is likely a scam and you should never respond to such an alert to avoid getting infected with malware.

• Only update Firefox via "Help > About" or by downloading and installing Firefox from the Mozilla server and never via a pop-up or link on a web page.
• plugins should only be updated via the plugin itself or by visiting the home page of the plugin.

zlennyz said

A screen with the Firefox logo appeared saying there was an update available for Firefox. I clicked the link and downloaded the file. Norton scanned the file and declared it unsafe and would not install it. The screen with the update appeared again and I overrode Norton and installed the update. Norton said it was unsafe and wanted to remove it. Was it a Firefox update or a scam. ?

Was the file name something like firefox_update.exe or firefox_patch.exe ?

This fake .exe over time is said to install things like viruses, trojans or unwanted software. Sites popup on occasions to target inexperienced Firefox and or Windows users in trying to trick them into downloading and running said fake update .exe without scanning it first.

Firefox is not just for Windows as it is for Mac OSX and Linux also so using .exe would not be an effective way to send out Firefox updates. The updates are done internally in Firefox (with a .mar file as you can see here for example) or by download from mozilla.org like say www.mozilla.org/firefox/all/

Even if Mozilla were to use .exe for Firefox updates on Windows, they would be serving them from a *.mozilla.org url and not from random websites with weird names and long random characters on url.

If you did run this fake .exe as you said you overrode Norton to do so, then you may want to scan your system with Norton and below software.

You can try these free programs to scan for malware, which work with your existing antivirus software:

• Microsoft Safety Scanner
• MalwareBytes' Anti-Malware
• Anti-Rootkit Utility - TDSSKiller
• AdwCleaner (for more info, see this alternate AdwCleaner download page)
• Hitman Pro
• ESET Online Scanner

Microsoft Security Essentials is a good permanent antivirus for Windows 7/Vista/XP if you don't already have one. Windows 8 has antivirus built-in already.