Sprinkle some dried, ground up eggshell around the plant on top of the soil. Do this after about a year, and then repeat every year. This will refresh the plant.

White powdery mildew on the surface of the soil?

Rosemary needs good air circulation. Without this, rosemary plants can develop a mildew that looks like a white powder. This is especially common if the air is humid. If this occurs then try and increase the circulation by placing a fan in the room for a few hours a day.

Aphids or spider mites?

Indoor rosemary plants are particularly prone to these. This is easily treated by spraying the plant with an insecticidal soap bought from a garden centre under the plant is healthy again.