Petey

Petey is the symbolic arch enemy of good, though he is usually just stupid instead of actually evil.

The Cops

The police officers are the symbolic good guys of the novels, including Dog Man. The reader fully expects the police to win every battle against the villains.

Firing the Chief

The Mayor's decision to fire the Chie is symbolic of the fact that she is an evil mayor with an evil plan.

The Chief's Hat

The Chief's hat is symbolic of the person in charge of the police. When a new Mayor arrives with plans to name someone as Chief, the Mayor is carrying the Chief's hat. This indicates he is planning to literally put it on the person he chooses as Chief. Dog Man runs away with the hat and hands it to the Chief, which puts the Chief back into the position of authority...