Most remodeling and cleanout debris is fine. The limits come from Wisconsin's landfill bans and from what the receiving landfill will take.
Wisconsin bans a long list of items from its landfills. That list covers electronics, car batteries, large appliances, used oil filters, waste oil, tires, and yard waste. Cans, bottles, cardboard, and newspapers are banned too, since they must be recycled. The City notes that cell phones are also banned from Wisconsin landfills.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
Refrigerators, freezers, air conditioners, and dehumidifiers need special handling because of the Freon. Brush and leaves should go to yard waste programs, not your container.
If you're not sure about an item, ask your account manager before it goes in.