I would like to automate these tasks as much as possible. Here is my list of topics.
1. Make sure that logging is working and the gateways are not logging locally. See sk38848 for logging troubleshooting info.
2. Do not use your gateways or management server as file servers. Delete any unnecessary upgrade etc. files after they are not needed anymore.
3. If you have a lot of logging, consider setting up a separate logging server (instead of taking all logs to your SMS or CMA).
4. Consider setting up a separate server for SmartEvent if used.
5. Manage the disk space on your management and logging servers to prevent them from filling up. See the following screenshot. Indexing logs takes space. It usually makes sense to delete the old indexes after a certain period.
6. Do not keep unnecessary database revisions
7. Keep your policies and databases as small as possible. Delete unnecessary unused or duplicate objects. Make sure all policies are assigned to gateways and remove the ones that are not needed etc.
8. Take regular backups and move them out of the box.
9. Monitor the system with SNMP.
10. Test your HA regularly