You are smart to be suspicious. Could you check to see whether an unnoticed add-on crept in? In particular, I suggest disabling ALL nonessential or unrecognized extensions on the Add-ons page. Either:

• Command+Shift+a
• Tools menu > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Usually a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that get rid of the nagging dialogs?

Don't do anything! They're trying to entice or scare you into installing something that isn't an official update from Mozilla, and will install unwanted Malware on your computer instead (or on a Mac might not do anything).

Firefox doesn't use "popup windows" for notification of an update being available. It uses an in-browser message bar. Sorry, I can't show you a screenshot of what that message looks like; I do manual updates on the morning each new version is scheduled to be released and haven't seen that message for a number of years.

Thanks to you both. I did check my add-on section and I had a mysterious add on enabled called "searchme 1.9" I know for a fact I did not put that there because I don't use add-ons at all. I disabled it and don't seem to be getting the annoying popup.

Thanks again :D