Most remodeling and cleanout debris is fine. The limits come from Ohio's landfill rules and from the facility that receives your load.
The Ohio EPA says trash landfills can't accept hazardous waste, PCB waste, bulk liquids or wastes with free liquids, scrap tires, or yard waste. Keep tires, leaves, and brush out of your container.
The standard exclusions also apply. Paint, solvents, fuel, motor oil, and asbestos stay out.
Appliances that hold Freon need the refrigerant removed and tagged by a certified technician before disposal.
Lorain County also runs a Collection Center at 540 South Abbe Road in Elyria for county residents and businesses. It doesn't take construction debris, furniture, or general trash, but its list of accepted items can help with some things that don't belong in your dumpster.
If you're unsure about an item, ask your account manager before you toss it.