Most remodeling and cleanout debris can go in your container. Wisconsin's landfill bans are strict, and they apply to every container in the state.
The Wisconsin Department of Natural Resources bans a list of items from landfills, including electronics, lead-acid batteries, major appliances, used oil filters, waste oil, and waste tires. Yard waste is banned too, including grass, leaves, garden debris, and small brush. So are everyday recyclables like cardboard, cans, glass and plastic bottles, and newspapers.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Pressurized tanks need their own disposal route as well.
If you're unsure about anything on your list, ask your account manager before it goes in the container.