Are the sites on the same version of PHP or MODX? What Dashboard widgets have you got installed? Some older dashboard widgets will silently fail and have no exit at failure like old versions of Google Analtics Dashboard and Quickbuttons. Usually you’ll see the 500s in the server’s error log vs in the MODX error log.
Some Extras may also require reinstall, you may be able to access the Extras Installer by going to manager/?a=workspaces.