The only thing I can think of that might be acting as a "hidden" GMail notifier is a Live Bookmark (though, then, why are you having trouble with GMail's certificate?).

I also have the same alert, but GMail is opened in a tab of my browser.

Phil, you're absolutely right – I had Gmail as a live bookmark! This must be the reason why it starts connecting at seemingly random times in Firefox.

Yup, same problem here. It worked yesterday. I started having problems around midnight. I guess it's just a new CA certificate or something.

I contacted Google about it but haven't received a response yet (they probably get lots of reports for this thing).

Chances are it's not a problem...

I'm getting the same problem when I visit https://gmail.google.com

same here.

the problem first appeared a few hours ago, then after a few futher attempts it went normally, and now it's again the same security altert.

I suggest all gmail users wait till this is fixed an not to enter their passwords.

Same problem, when I visit gmail.google.com

Some Root-Certificate seems to be outdated. Wait for an update for Firefox. Blue arrow top right.

It seems ok now, no more alerts.