Most remodeling and cleanout debris is fine to load. The limits come from Kentucky's landfill rules and from the facilities that take your load.
Kentucky's Energy and Environment Cabinet permits separate landfills for household waste and for construction debris. Landfills for construction debris take only non-hazardous building and demolition waste, so mixing in household trash or chemicals can cause a load to be turned away.
On top of that, keep hazardous waste, liquids, paint, solvents, fuel, and asbestos out of a standard dumpster.
The city's regional transfer station also refuses asbestos, all batteries, contaminated soil, liquid paint, pesticides, free-flowing liquids, and anything containing mercury or Freon. Tires and appliances cost extra there. Lead paint can only go to a household hazardous waste collection event.
If you're unsure about an item, check with your account manager before you load it.