Most remodeling and cleanout debris is fine to load. The limits come from Missouri's landfill bans and from each facility's own rules.
The Missouri Department of Natural Resources bans several items from landfills. They include major appliances such as refrigerators, freezers, washers, dryers, stoves, dishwashers, and water heaters. Whole tires, oil, and lead-acid batteries are banned too. Microwaves are the exception and can be landfilled.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. In older homes, asbestos can show up in pipe insulation, floor tile, and siding, so test before demolition.
If you're not sure about something, ask your account manager before it goes in the container.