Most household junk and building debris can go in your container. Minnesota's landfill rules and the county landfill's policies set the limits.
Minnesota landfills aren't allowed to bury liquids, hazardous waste, fluorescent bulbs, tires, major appliances, vehicle batteries, motor oil, or oil filters. Electronics with a screen, like TVs and computer monitors, are on the list as well. State rules ban tires from land disposal outright.
That doesn't mean you're stuck with those items. The Steele County Landfill takes appliances, tires, TVs, and monitors for recycling, each for its own fee, so they're handled separately instead of going in the pit. Mattresses are also charged by the piece.
Paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Asbestos is handled at the landfill under its own rules and fees.
Before you load anything you're unsure about, check with your account manager.