Today I locked a Windows Server 2003 console session at a client site, then tried later to access the console session by typing “mstsc.exe /console” from the command line. Instead of connecting to the console, I found myself dropped into a new session on the server. When I started Terminal Services Manager on the remote machine, I saw two sessions, including the console session. When I tried to remote control the console session, I got the message, “”Can't remote control session (ID 0).”

I finally found this Terminal Services Team Blog post with the explanation:

Changes to Remote Administration in Windows Server 2008

There are reasons why /console is no longer needed in Windows Server 2008. Apparently that justifies removing this functionalitiy from RDC 6.1, even when connecting to Windows Server 2003. Worse, the connection succeeds but “silently ignores” the /console switch.

Fortunately, there is a workaround:  use the new /admin switch instead.

Both the application-specific Help file and the Windows XP Help and
Support Center still list the missing /console switch and do not mention the
/admin switch. Note to Microsoft:  if you're going to “silently” remove functionality, at least update the documentation!