Most renovation and cleanout debris is fine. Wood, drywall, plaster, shingles, flooring, cabinets, brick, furniture, and general junk all go in.
The Commonwealth of Virginia draws one hard line that catches people out. It is unlawful to put a used lead acid battery, which means any wet cell battery, into mixed municipal solid waste. The state's own waste law sends them to a retailer, a wholesaler, a smelter, or an authorized recycler instead.
Arlington County's waste rules exclude household hazardous materials by name, and the county's definition covers paints, stains, varnishes, solvents, and pesticides. Those stay out, along with fuel, propane tanks, pool chemicals, used oil, and asbestos. The regional transfer station does not take commercial hazardous waste at all.
One more Arlington rule is easy to trip over. The county bars mixing trash with any source-separated recyclables or organics set out for collection, so keep a cardboard or yard waste pile separate rather than tipping it into the container at the last minute. If an item has you guessing, ask your account manager first.