I have a forced air, gas fired heating system. I have had the same system in other systems without the same problem; that is, this house has dust accumulation that is far greater than I am accustomed to. I have changed the filter in the heating system, but it doesn't seem to help. Any ideas?

You may want to try a better filter. Or may even want to have a filtration system installed. It wouldn't hurt to have your heating system(furnace and ductwork)cleaned by a pro. Lots of things could be causing this. Not sure I would blame the furnace. But installing a better filter, or even a better filt system, would most likely help.