How can I be a good office administrator?

Use a validation rule to do a VLOOKUP of the Billing Postal Code to a custom object that maps postal codes to states/provinces.
Use a trigger that populates Billing State/Province based on a custom object that maps postal codes to states/provinces.

Confirmed: https://www.proprofs.com/discuss/q/95167/administrator-universal-containers-wants-improve-data-qualit