mozar,
You will need to:
1. Review the lease. If you used a good standard form lease designed for your area, this situation should be well described. My leases have a clear $$$ per day rate for staying past the end of the lease or staying past the last day given in the 30 day notice.
2. State and local law will govern the allowable charges. In most cases you can assess the partial month against the security deposit if an explicit fee isn't detailed in the lease.
Be sure to clearly document the move out date by keeping copies of all written communication. Require all changes in move out dates to be in some form of verifiable communication. Written and signed is preferable, but email and screen shots of text messages should suffice.
I have had wonderful tenants, and have never had a move out issue that wasn't resolved well in advance. I would be hesitant to pursue a small rental deficit. Attorney fees could eat up any expected gain of the former tenant decided to challenge anything.