Most construction and cleanout debris is fine. South Carolina law and the county's rules decide what stays out.
Under state law, used oil and lead-acid batteries can't go in regular trash. South Carolina also bars TVs, computer monitors, and computers from landfill-bound waste. Landfills there can't knowingly take a load with more than a trace of those devices, so pull them out before loading.
York County's construction and demolition landfill also turns away food waste, tires, and anything containing asbestos. Tires are handled separately and only by appointment.
Standard exclusions apply too, including hazardous waste, liquids, paint, solvents, and fuel. If you're not sure about an item, ask your account manager before it goes in the container.