Ordinary household and construction debris loads without any problem. The limits come from the landfill's own refusal list and from Virginia law.
The county landfill turns away railroad ties, fertilizers, fuels of any kind, and lead acid batteries. Chemicals, cleaners, cooking oil, fluorescent bulbs, oil based paint, and medical waste are only taken on the site's hazardous waste days, not with a regular load.
Latex paint is a common mistake. The landfill only takes it once it has completely dried out, so open the cans and let them harden well before the container is picked up.
Virginia law also makes it unlawful to put a used lead acid battery in household trash. Car and truck batteries go back to a retailer or wholesaler, or to an authorized recycler.
Hazardous waste, liquids, solvents, fuel, and asbestos stay out of any standard container. If you are unsure about an item, ask your account manager before it goes in.