There are two main qualities that a person needs in order to be a good police dispatcher.
First, a person needs to be able to maintain his or her composure under pressure. This job can, at times, be very stressful. There will be long periods of time when it is fairly boring as nothing is happening. But then there can be very stressful periods when there are many calls at once or when something really big is happening. A dispatcher has to be able to maintain composure and focus at these times.
Second, a person needs to be a good communicator. This means that the person needs to be able to give the police officers the information they need in a way that is easy for them to understand. It also means that the person needs to be able to get information from police officers. This is an important part of the job as the dispatcher must handle the egos of the police officers and the fact that they might be in stressful situations. The dispatcher needs to communicate well enough to get the necessary information from them.
These are the main qualities needed to do this kind of work.