Most household and construction debris loads without any trouble. The limits come from Colorado's disposal rules and from ordinary safety.
The state keeps a short list of materials that may not go to a landfill. It covers lead-acid batteries, liquid waste or anything holding free liquids, used oil, waste tires, and electronic devices and computers. That last one catches people out, since old televisions and monitors turn up in nearly every basement cleanout.
Hazardous waste is out of every container as well. That means paint, solvents, fuel, pesticides, pool chemicals, and asbestos. Appliances holding refrigerant need to be handled separately too.
Jefferson County residents have a good local option for all of it. The Rooney Road Recycling Center, owned and operated by a coalition of cities and towns in the county, takes household chemicals, solvents, paint, fertilizer, used oil, and electronics. Appointments are needed for household hazardous material, and the number is 303-316-6262.
Set those items aside before the container is loaded. If something has you unsure, ask your account manager rather than risking a load being turned away.