Most remodeling and cleanout debris can go in your container. The limits come from standard disposal rules and from how Dover handles certain items.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
Dover sends several household items to its Recycling Center instead of the trash. TVs and microwaves must go there, and each carries a disposal fee. Monitors, printers, and other computer gear have set fees there, too. Car and boat batteries belong there too, along with antifreeze, mercury thermometers and thermostats, fluorescent bulbs, and tires.
Appliances with refrigerant, like fridges and dehumidifiers, carry their own fee at the center. Pull those out before you load the container, and mention any tires or appliances when you book.
When in doubt, check with your account manager before an item goes in.