The best part is that, if you're logged into an apps account that isn't provisioned for the service, it tells you to log in to another account. Then you log into that account and it tells you again to log in to another account. etc.
I've told some Googler friends about this, and I think they're filed bug reports, but the new fancy multi-account sign-in thing remains terminally broken. It's been bad for at least a year, I think.
My (partial) solution: all of my cookies are wiped every time I restart my browser. It turns out they're not all that important.