Most construction and cleanout debris is fine to load. The limits come from Louisiana's landfill rules and from what the parish landfill accepts.
Louisiana bans several household items from landfills. Lead-acid batteries, used oil, whole tires, and small sealed lead-acid batteries all have to be recycled or dropped somewhere else. Tires have their own limit at the parish landfill as well.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. The parish landfill turns away hazardous waste, industrial oil, grease, farm chemicals like fertilizer and pesticide, regulated asbestos material, and burn barrels. Paint is only accepted when it's fully dried out with the lid off.
If you're unsure about an item, ask your account manager before it goes in the container.