Most construction and cleanout debris is fine to load. The limits here come from a strict statewide rule and from what the county facility will take.
Wisconsin is unusually firm about this. State recycling law bans a list of materials from being landfilled or burned anywhere in the state, in homes and businesses alike. The banned list covers cardboard and containerboard, office paper, newspaper, magazines, glass containers, steel and aluminum cans, number one and two plastic containers, electronics, major appliances, lead acid batteries, used oil and oil filters, waste tires, and yard waste including brush under six inches across. Those need to come out of the load, not go in it.
The county facility adds its own refusals. It will not take asbestos, medical waste such as needles or medication, items with radioactive material like smoke alarms and exit signs, fire extinguishers, or yard waste.
Standard exclusions apply as well: hazardous waste, liquids, solvents, fuel, and wet paint. Stevens Point requires latex paint to be dried solid before it goes in the trash at all, and the city bars burning or burying demolition material, electronics, appliances, tires, and paint on any property in town.
Not sure about something in particular? Check with your account manager before it goes in the container.