To clean a room thoroughly, work clockwise around the room cleaning from top to bottom. This keeps you from jumping around and loosing time, and any dirt and dust that falls from the higher areas will fall on surfaces that are yet to be cleaned.
Do you line your wastebaskets with plastic trash bags? Keep a few extra new bags in the bottom of the wastebasket so that when you throw out the full bag, you have a new bag ready and waiting. For small wastebaskets, use plastic shopping bags as a cheap alternative to commercial trash bags.
New cloth diapers make excellent cleaning cloths. They are highly absorbant, are easily washed and bleached, and are often used by professional cleaning services. Since buying a package of diapers for this purpose, I now use nothing else and have eliminated most of my odd assortment of rags for a neat stack of diapers.