Most construction and cleanout debris is fine. The limits come from Alabama's landfill rules and from the landfill that takes your load.
Alabama rules keep regulated hazardous waste and free liquids out of regular landfills. Starting after 2027, whole tires can't be landfilled in the state either, so it's best to keep tires separate now.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
The New Georgia Landfill also refuses paint, oil, gas, fluorescent bulbs, batteries, small engines, pressurized tanks, and appliances holding refrigerant. The City's curbside service won't take electronics, and its recycling center on First Avenue North takes cardboard, plastics, and newspaper.
If you're unsure about an item, check with your account manager before it goes in.