It appears that a few people have had the problem where everything works great in agent desktop, but not when selecting a contact to work with, as they get some thing like
The underlying connection was closed: The remote name could not be resolved.\n\nStack:\n at Microsoft.Ccf.Csr.Sessions.SetActiveSession(Guid sessionID)
at Microsoft.Ccf.Csr.Sessions.AddSession(String name, Int32 callID, Object customer)
at Microsoft.Ccf.Samples.Csr.AgentDesktop.Desktop.AddSession(CustomerRecord customer, CallClassProvider call)
and/or
Customer Care Framework 2005 - Agent Desktop: Error: Failed to connect to the web server. Please verify that you can connect to the web server.
Well it would appear from the outside that the SetActiveSession method (atleast in the .Net 1.1 QFE 3 version, and likely the earlier .Net 1.1 version) has the server hard coded (since this is one of the few assemblies you don't get the code for and reflector wasn't much help in finding out I can not state for sure).
If it is hard coded it is insanity and *hopefully* fixed in the .Net 2.0 release. But if you do hit this because your CCF server is not named CCFIIS the simple fix is either add an entry to the DNS server on your network to redirect to that or (if you can't due to security restrictions during development) add it to the hosts file in c:\Windows\System32\Drivers\Etc\
Once that is done, restart agent desktop and enjoy.
Update:Thanks to MattB on the CCF Forum for confirming it is hard coded and that a hotfix is available for 1.1 from PSS and 2.0 is already fixed :)