Most remodel and cleanout debris is fine. North Dakota law and the City's landfill rules set the exceptions.
North Dakota law says lead-acid batteries, used motor oil, wind turbine blades, and major appliances can't be thrown away in a landfill. Major appliances include refrigerators, freezers, washers, dryers, stoves, water heaters, furnaces, and air conditioners. The City's landfill takes appliances at a separate per-item fee so they can be recovered.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Tires and electronics are accepted at the landfill for a per-item fee, so keep them out of your mixed load and mention them when you book.
The landfill also cares how loads arrive. Untarped or unsecured loads are charged an extra fee and can be turned away.
If you're not sure about an item, ask your account manager before tossing it in.