Daily - I scan the application log for errors that would impact the BES .. hung threads etc. As noted watch for anyone who's disabled / removed from AD and not removed from the BES .. BES don't like that
There is a document that outlines events that can impact BES performance, though it's kinda outdated and written for BES 4.0
Verify all services are running. I have BES Alerts configured as well MessageConfirm so I get a message every 15mins. If you want to really do a full check send yourself an attachment and verify conversion / open. The AdminKit also has tools so you can track the speed of your BES. The coming monitoring service will be a godsend for this.
Check for HD space, the log files fill up, I like to keep a couple weeks worth for review, troubleshooting.
Monthly - Audit for non usage, last contact greater then 15 days gets an email if they are using their device and if they have an issue. If needed clean off old accounts, people that havn't activated in your alloted time to.
Also I have Diskeeper running as needed between 1am - 5am.