The scope will not be known. The exact situation will not be known until well into the event.
Some of the worst-hit areas might be the last to be responded to. Decisions will have to be made in the absence of complete information.
Communications will fail. There are over 30 types of communications failures; most large emergencies will suffer multiple types of communication failure. From infrastructure damage, to system overload, to information not getting to the person or not arriving in time to misunderstanding what someone else said, communications will fail.
Situation constantly changing. What you are responding to might have significantly changed by the time you actually arrive on scene. The events of 9/11 offer an example of how quickly things can change from the start to the finish of an event.
Emergency services will be affected. A police car is no better than a passenger vehicle when whiteout conditions occur on a highway. Flooding blocks the road for an ambulance as much as any vehicle. A fire hall is equally likely to be damaged by a tornado as any structure.
Unusual response required. If the emergency services are affected, then alternate strategies might be required. Disasters commonly have pictures of someone doing something unexpected, but successfully, when your regular response isn’t working.
Massive Convergence. Convergence of organizations, volunteers, off-duty personnel, government officials and outside media can be truly breathtaking, with hundreds of organizations arriving for a major emergency, let alone a disaster. Emergency services are often unprepared for the size of the response in support of their operation.