Most debris from a remodel or cleanout can go in your container. Maine's disposal rules and the facility that takes your load set the limits.
Maine treats several common household items as universal waste, and they can't be thrown away. The list includes rechargeable batteries, mercury thermostats and other mercury devices, fluorescent and other mercury bulbs, some light ballasts, and leftover oil-based house paint.
Screens have their own rule. The Maine Department of Environmental Protection says it's illegal to throw away cathode ray tubes and LCD screens. That covers old TVs, monitors, laptops, and tablets, which go to electronics recycling instead.
Hazardous waste, liquids, solvents, fuel, and asbestos aren't allowed in a standard dumpster either. Pull out the TVs and batteries before loading, and flag mattresses, tires, and Freon appliances when you book, since local facilities charge for them by the piece.
Check with your account manager if anything on your list seems uncertain.