Most building and cleanout debris loads without a problem. The limits come from New Mexico's solid waste rules and from what the municipal landfill turns away at the gate.
New Mexico keeps lead-acid batteries out of every landfill in the state. Liquid waste is barred too, other than small household containers, and so are medical waste, radioactive material, and hazardous waste bound for a facility that isn't permitted for it.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. The Roswell landfill also refuses explosives and ammunition, unknown chemicals, highly flammable or toxic material, paint, motor oil, and manufacturer or industrial chemicals. It does take clearly labeled household oil, gas, and paint when dropped off separately.
Tires need to stay out of the container as well. If you're unsure about an item, ask your account manager before it goes in.