What has caused the leaves of my African violets to be covered with some sort of white material?
From your description, this white film is probably powdery mildew, a fungal disease. Its usual causes are excessive humidity and poor ventilation. Dead flowers often trigger the spread of this disease, which is contagious, so isolate or discard infected plants. Reduce watering without harming your plants and improve air movement in the area. Handle infected plants as little as possible. Do not use infected plants as the source of material for propagation.