Ordinary building and household debris is fine. The limits come from New York State law and from the two public facilities that receive Watertown loads, and the facility list here is longer than most.
New York bans consumer electronics from the trash entirely. The state's rule is that since January 2015 consumers can no longer throw out covered electronics in landfills, waste-to-energy plants, household trash, or at the curb. One old TV buried in a full container can send the whole load back.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are out of a standard container as well.
The regional landfill that takes Watertown debris also turns away a long list of everyday items: waste tires, lead acid batteries, rechargeable batteries, used oils, white goods like refrigerators, stoves, and air conditioners, scrap metal including vehicles, leaves, grass, branches, and stumps, sealed containers, pesticides, herbicides, and hot ashes. Its published rules also size the heavy material: concrete pieces should be no bigger than two feet by two feet with no rebar sticking out, and steel, piping, and dimensional lumber should be cut to eight feet or shorter. Painted or treated building material from anything other than a house needs screening approval first.
That is a lot to track, so tell your account manager what the job will produce and they will flag anything that needs its own trip.