Hi Dan,
There are some users have the similar upgrade notification that you reported when using O365 sign-in page. We are definitely looking into this. It is currently being investigated and we will be updating you as soon as possible. We really do appreciate your patience and apologize for any inconvenience.
Starting in October of 2012 and extending into early 2013, we be rolling out a service update to existing online services customers that will add new, richer experiences to SharePoint Online and Office Web Apps. Internet Explorer 7 can't deliver these experiences. That’s why you will be able to see this message and inform you to upgrade IE Browser. So far, all the services are running smoothly even you are using IE7. If the Internet Explorer version you are using is above 7. You can ignore this message and continue to use your services on Office 365. If you are using IE7, it would be very nice that you can upgrade to latest version of Internet Explorer now.
Office 365 is ending support for Internet Explorer 7 after Oct 1, 2012. Further information can be seen in the article provided by Cherry.
Regards,
Reken Liu