I am using superduper to mirror my server harddrive nightly. Should I be shutting down the mail services before I do this.
Or any other service?
OS X server uses Postfix for mail. It's reasonably safe to back up a host while Postfix is running. After restoring the queue may be a little messed up. These queue problems can be repaired by running
Regarding other services: Hard to say without knowing what other services you're running. Databases, for example, frequently require special care when backing up.