Microwave cooking of food is not harmful, based on current research. In fact, microwaves preserve more of the vitamins and minerals in food because the food’s exposure to heat and water is shorter than with conventional cooking methods. Here is information from the USDA Use Your Microwave Safely.
Microwaves cause the water, fat and sugar molecules in food to rotate rapidly and bump into other molecules which produces heat and cooks the food. What initially scared consumers about using microwaves was the warning on the door about radiation if the door was open and a mesh screen covering the glass door. All microwave ovens have a safety mechanism that prevents you from operating the oven with the door open.
The only person who should not use a microwave oven is someone who has a heart pacemaker implanted. The microwave could disrupt the electrical impulses produced by the pacemaker.