That's a new record!
If you have a .Mac record in your keychain Aperture tries to connect to it -- even if the account is long defunct.
When that happens it displays an alert "There was a problem connecting to .Mac". You can't get the alert to go away, in fact I now have multiple floating dialogs telling me of this problem.
I'm going to try pulling my network cable next time I restart.
They ought to be ashamed, but as far as I can tell Apple is shameless.
Update: I quit, pulled the network cable, and restarted. It hung on start but after a minute or so something timed out and it did run correctly. I then restarted with the network cable and got the looping error message. I'll probably have to locate the .mac entry in my keychain and remove it.
Update 2/13/08: The fix for now is to open the .Mac preferences in your System Preferences. Remove your old username and password for the inactive account. The bug goes away.