https://support.mozilla.com/en-US/kb/Websites+or+add-ons+incorrectly+report+incompatible+browser

I've been using Firefox for...a long time now. I think I noticed the 'You're not on the latest version of Firefox...' message around v.4. I update within days of any new release. I'm too lazy to try the obvious things, uninstall/reinstall, delete profile, etc, or maybe due to my profession (computer-person, full time + self-employed consultant) I may want to just find that pesky file entry in the chrome or somewhere that isn't correct. Has anyone identified where the offending entry is?

The text about not running the latest Firefox version is in the code of the www.google.com/firefox site that previous Firefox 3 versions use as the home page and it looks that Google no longer maintains that page.
Current Firefox 4+ versions no longer use that Google website as the home page, but use the build-in about:home page as the home page.
Google assumes that you use an older Firefox version if you still visit that site and warns you that you use an older Firefox version and suggests to update.
You can ignore that message if you run the latest Firefox version as reported in the Help > About window.
You can use another page as the home page like about:home or www.google.com or www.google.com/ig (iGoogle).

I take it from the looks of things as the last post was 4 months ago, nobody's bothered to even look into this and provide a solution, or even a means to make it stop showing the message.

Colin.Warren, is your homepage set to the old Firefox start page (in Tools->Options->General) as in say http://www.google.com/firefox/ as this is where the OP nancyf and the poster MrL0gistiX is seeing the "You're not on the latest version of Firefox" message.

This old page is maintained by Google and is no longer used as the default homepage ever since Firefox 4.0 has been about:home

I get this with plugins.

Found:

plugins.hide_infobar_for_missing_plugin

plugins.hide_infobar_for_outdated_plugin

Set those to TRUE

Got rid of the annoying message about Flash 11.2.202.235 being out of date.

Then this thread is not related to your issue.

This thread is the only one that manages to be found when searching for an answer, anyway, got rid of the message, see above.