Ordinary construction and cleanout debris loads without trouble. Lumber, drywall, siding, shingles, flooring, tile, cabinets, doors, windows, furniture, carpet and cardboard are all fine, and clean concrete, brick and block belong in the smallest unit.
The hazardous list stays out: paint, stains, solvents, thinners, fuel, motor oil, antifreeze, propane cylinders, pool chemicals, pesticides, asbestos-containing material, wet batteries and liquids of any kind.
Paint is a special case here. The county landfill runs a paint recycling service, but only for oil-based paint, only for Wilson County residents, and only twice a year, with no commercial loads at all. Latex paint is not accepted; the County's guidance is to dry it out with hardener or cat litter until solid, after which it can go out with regular trash. So a container is not the route for paint cans unless they are dried solid.
Electronics are better placed than most people expect. The county landfill takes televisions, computers, printers and microwaves, so a sorted pile of old equipment has a home rather than needing to be buried in a mixed load.
Tires and automotive parts are refused at the county convenience centers and should be kept out of a container as well.
If something is borderline, say a part-used tin of deck stain, a sealed drum or a water heater, run it past your account manager before it goes in.