Most of what a build or a cleanout makes is fine to load. The limits come from state rules and from what the county landfill will take at the gate.
New Mexico's solid waste rules bar lead-acid batteries from any landfill, and they bar infectious waste and radioactive material outright. Liquid waste is allowed only in narrow cases, which in practice means no liquids in a roll-off container. The rules also forbid taking any waste to a facility whose permit does not cover that waste, which is why the gate can turn a load away even when the material is legal somewhere else.
Hazardous waste, paint, solvents, fuel, used oil, and asbestos stay out of a standard container. So do appliances holding refrigerant until a technician has recovered it.
The county adds its own refusals. Tires over 24 inches are not accepted at the landfill at any price, and scrap wire has to be cut into three-foot lengths before it will be taken.
Carlsbad also will not collect construction debris, tires, car body parts, or large appliances from a city container at the curb, which is exactly why a project load needs a roll-off. If you are unsure about an item, run it past your account manager first.