There are two ways to fix these common entourage errors.
First- try holding down the option key when you open Entourage. It will pop up with the database utility.
Click on "rebuilt database" and continue. Once that's done, try opening entourage normally and see if the items sync.
If that doesn't work, and all of the users information is on an exchange server (which, according to your screenshot, it looks like it is), try completely removing the entourage account in the "Entourage" --> Account Settings window and then re-add it.
