I have the same problem, whenever I try to signin my existing account or signup new one, Lumia 620 keeps saying "NETWORK PROBLEM. We couldn't complete that operation. Please try again later."
It is really very frustrating for new WP users.
I had problem with my Nokia account.... Every time i wanna add Nokia account to the phone it keeps telling me network error :/ when i,m already connected to the net
Check whether you have the latest version of the app, it was recently updated.
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its the same problem with my phone even.. and nokia is missing out the basic functionalities that it has to provide like call duration info, profile settings, contacts copying, and many more..
Can't access my Nokia account on my Lumia 620 neither. From all the entry points (Nokia Pulse Beta app, via settings...) it just keeps getting stuck at "Connecting..." animation going on forever. No error message.