Most construction and cleanout debris is fine. The limits come from South Dakota's landfill ban and from the City's own rules.
State law bars South Dakota landfills from accepting yard waste, car batteries, waste motor oil, and large appliances such as washers, dryers, and refrigerators. Tires can only be landfilled once they've been processed.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
The City also warns about fire risks. Lithium batteries, hot ashes, aerosol cans that aren't empty, and old fireworks should never go in a container. Flammable chemicals go to a City household hazardous waste event instead. City code also keeps tires and yard waste out of any container collected by a licensed hauler.
Appliances are worth singling out. The City landfill accepts none of them for burial, Freon units included, and anything it does take has to be recycled instead. A Freon appliance is only taken for recycling with written certification that the refrigerant was properly removed. If an appliance turns up in a load at the landfill, the hauler has to pull it back out at their own cost, which is why we ask about them up front.
Food waste and anything else likely to rot has to stay out as well. Rapid City requires wet material of that kind to move in an enclosed packer truck rather than an open container, so a roll-off is the wrong tool for it.
If you're unsure about an item, check with your account manager before you load it.