Possible Clues:

• Our mortal body, do you say?
• Powdery material
• Objects may collect it; people, probably less often
• Dry mop target
• Neatnik's bane
• Beach produced it, and it was on the sea
• It settles indoors
• Does thou sound as if thou be in little bits?
• Sign of poor housekeeping
• ... and, after a 1 across, Springfield to suffer fool badly