Most construction and cleanout debris loads without trouble. The exclusions are the usual safety ones, and the Town publishes a particularly clear list of what needs its own route.
Hazardous waste, liquids, solvents, fuel, used oil and asbestos stay out of any container. Oil-based paints, stains and varnishes are out too, because their solvents release fumes and can contaminate groundwater. Household cleaners, including bleach, ammonia and drain and oven cleaners, and all pesticides, herbicides and fertilizers need the hazardous waste route rather than the container.
Batteries deserve their own mention, and the Town's reasoning is worth repeating. Alkaline, lithium, rechargeable and car batteries all contain heavy metals and corrosive material that leach into soil and water, and the Town notes that they spark fires in trucks and landfills. That is a real risk to a loaded container on a hot day here, so batteries come out before the hauler loads.
Tires and appliances holding refrigerant should be kept separate and mentioned when you book. If you are unsure about an item, ask your account manager while the container is still empty.