Normal house and jobsite debris is welcome. The limits come from Minnesota law and from the facilities that receive the load.
Minnesota treats demolition debris as its own waste stream. The state defines it as concrete, brick, bituminous concrete, untreated wood, masonry, glass, trees, rock and plastic building parts, and it expressly does not include household garbage or asbestos. Asbestos is a live issue in Brooklyn Park's older housing, so have it tested and handled separately before any tear-out starts.
Burning is not an answer here either. State rules bar burning treated lumber, composite shingles, tar paper, insulation, sheetrock, wiring, paint, tires and plastics, and the city bans burning garbage or yard waste outright.
Hazardous waste, liquids, paint, solvents, fuel, used oil, batteries and tires stay out of your container. The county runs a drop-off site for exactly those household items, which is the right route for them.
If an item seems borderline, ask your account manager before it goes in the container. It is far cheaper to pull one item out in the driveway than to have a load refused.