Well, security would be the first concern (one never
knows whether the old admin would try to do harm).
Change roots password, make sure there's only
one root account, disable any accounts that are
obviously unused, or might be used by others.
Make sure /etc/shadow hasn't been set world-readable.
Check /etc/hosts.allow /etc/hosts.deny
Look at ssh, rsh, rlogin (search for .r* files).
If you have any more specific questions ... ;)