Most construction and cleanout debris is fine. What is out comes from Missouri's landfill rules and from what the City's own facility will take across the tipping floor.
The Missouri Department of Natural Resources explains that sanitary landfills have to exclude certain wastes, naming hazardous waste, waste oil, large amounts of liquids, lead-acid batteries, appliances, and brush or other vegetation. Those limits follow the load wherever it goes.
The City's list is blunt about it. Tires, yard waste, paint cans with paint still in them, engine oil and other petroleum-based flammable liquids, asbestos, sealed barrels or drums, compressed or inert gas bottles, and hazardous chemicals are all refused, and the City notes that no amount of any of them will be accepted. A load that turns up with prohibited material carries a separate service charge, so this is worth a second look before the lid closes.
A few items need a different route rather than a ban. Flat-screen televisions are no longer taken at the City's recycling drop-off, and electronics and light bulbs go to the county program instead. Appliances with refrigerant carry a per-item charge, as do hot tubs.
If you are unsure where something falls, ask your account manager before it goes over the rail.