Most construction and cleanout debris is fine. The limits come from New Mexico's solid waste rules and from the regional authority that takes the load.
New Mexico doesn't allow car batteries at any landfill. The state also keeps liquid waste out of landfills, other than small household containers, and it bans petroleum waste and hazardous waste from regular disposal sites.
That means hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The regional authority adds its own rules: every load must be covered, and it won't take hot ashes or any hazardous waste.
City code also groups bricks, concrete, tires, tree limbs, and appliances as demolition waste that goes to a separate disposal area. Mention tires and appliances when you book so we can plan for them.
When you're unsure about an item, ask your account manager before you load it.