I had the same problem (when signing out of Hotmail).

I found that the problem was caused by my disabling third party cookies in Firefox.

I also found that the error message did not appear to be accurate. It says that I am not signed out of Hotmail. However, if that were true, then by clicking my bookmark for Hotmail (right after the message was displayed), I should be taken back to my Hotmail inbox. Instead, when I click my Hotmail bookmark (after receiving the error message stating I was not signed out of Hotmail), I was taken to the usual Hotmail sign-on page (which implies to me that I really was signed out of Hotmail).

My guess is that MS is using third party cookies to track ones browsing.

I do not want to enable third party cookies just to get rid of a bogus message from MS.

So, I just wrote a simple Greasemonkey script to bypass the page with the error message and display a blank screen when I sign out of Hotmail ... I am no longer bothered by the bogus message.

YMMV.