I struggled with this problem for a long time. My first solution was to just disable Offline Files on my network. I used group policy to ensure that Offline Files would never be used. Then I dug around some more and found problems relating to SMB Message Signing. Windows XP Service Pack 1 made SMB signing incompatible with Windows 2000's version of the same. The solution was to disable SMB signing on the server, which I did using the registry.
Now Microsoft has a fix for this problem disguised as a security hotfix. The solution is, therefore, to apply the hotfix described in Flaw in SMB signing may permit group policy to be modified and all should be much better. If that doesn't work, set the REG_DWORD value enablesecuritysignature in HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\lanmanserver\parameters to 0.
This was first published in March 2003