Most building and household debris is welcome. The limits come from New York law and from what the county landfill accepts.
Electronics are the firmest rule. New York bans covered electronic equipment from disposal at any solid waste facility in the state, so a television, monitor, or computer cannot simply ride along in the load. The state ban binds the facility as well as the customer, which means one old set can put a whole load at risk. Broome County takes electronics at its hazardous waste and electronics facility, free for county residents.
Hazardous material is out as well: paint, paint thinner and solvents, pesticides, acids, caustics, oil, and batteries. Binghamton lists all of those as prohibited material, along with tires and medical waste. The city also bars garbage or trash generated outside the city from its own collection stream.
Asbestos and tires need their own handling rather than a place in a mixed load. The county requires a transporter manifest for both, and it asks that non-friable asbestos be declared at the scale. Friable asbestos needs a call to the landfill before anything moves.
One rule applies to every load, not just unusual ones: under state and local law, loads arriving at the county landfill must be covered, and an uncovered load picks up an extra charge. Keeping debris level and under the rim is what makes that possible.
If you are unsure about something, ask your account manager before it goes in the container.