Most remodeling and cleanout debris is fine. The limits come from Missouri's landfill rules and from what the City's transfer station will take.
Missouri keeps several items out of landfills. That list includes major appliances such as refrigerators, freezers, washers, dryers, stoves, dishwashers, and water heaters, along with whole tires, used oil, and lead-acid car batteries. Plan to handle those separately.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos don't belong in a standard dumpster either. The City treats oil-based paint as hazardous waste. Latex paint is only allowed once it has dried out completely.
The transfer station also turns away concrete, railroad ties, car parts, pesticides, batteries, and tires. If your project includes broken concrete, ask about a separate plan for it.
Not sure about an item? Check with your account manager before it goes in the container.