Ordinary remodel and cleanout debris is fine to load. The limits come from what Virginia lets each kind of landfill accept and from what the regional facility here will take at the gate.
Under Virginia's landfill rules, a sanitary landfill may only receive nonhazardous solid waste unless its permit says otherwise, and a construction and debris landfill may only receive demolition waste, construction waste, debris waste, land clearing debris, split tires, and white goods. Nothing else is authorized. Tires have to be split or shredded before they can be buried, and asbestos from a renovation has to go to a facility set up to take it.
That rules out the usual suspects: hazardous waste, liquids, paint, solvents, fuel, motor oil, batteries, and pressurized cylinders. Whole tires and appliances holding refrigerant need to be handled separately, so mention them when you book.
For leftover chemicals, the town points residents to the New River Resource Authority's household hazardous waste collection events instead of the landfill or the curb. The regional authority holds a collection day for Montgomery County residents in November, by appointment.
Holding something you can't place? Ask your account manager before it goes in the container.