UPDATE: Apple published an updated version of the Security UPdate 2007-005 which automatically restarts your DNS server after updating BIND.
When you install Apple’s latest Mac OS X Server Security Update 2007-005, keep an eye on your DNS service. On my two servers DNS was deactivated after a restart, and I had to manually start it after the update.
It seems like the update process deactivates the DNS service to update BIND and then forgets to reactivate it after the update.