Give assignments for emergency situations
Do you have a phone tree plan (who calls who?) for key members of your family or work? If there are older kids in the family, put them in charge of something simple, like contacting the dog sitter.
Do you have a plan for a baby-sitter in emergencies? Assign someone to making that phone call.
Is there a plan for false alarms? Make sure part of your plan includes the "reverse" phone tree when such a non-emergency is resolved. Whoever is responsible for informing people should also be responsible for updating them.
Plan for scenarios where one or more of your family members are still in school or at a job. Do you have a meet-up point? Is someone assigned to pick up a member of your family from school?