You should have a filter in the furnace return air. If the vents are dirty from the air circulation, the furnace heat exchanger will be covered in dust and dirt along with all the ducting. If they are dirty from just foot traffic, removing them is probably the best way, otherwise the dirt will just fall into the ducting as you are brushing or cleaning them, and when the furnace fan is on, it would blow the dirt into the living space. JMHO.
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