There are actually a few ideas with this but it all revolves around appointment creation.
Creating Appointments via New by Staff
When you select a center the Staff section should be filtered by which staff work in that center. Currently you can select a center and pick ANY staff even if that staff does not work in that center.
Creating Appointment via Wizard
After choosing subject area the next selection should be center instead of services. This way when you get to the services screen only the services for that center show instead of showing every service. By adding the center it should also filter the staff based on center as well.