Most household and construction debris loads without a problem. The limits come from the Ohio Environmental Protection Agency's rules for the landfill and from that site's own refusal list.
The county landfill turns away hazardous waste, asbestos, liquid waste including motor oil and wet paint, lead-acid batteries, whole or shredded tires, televisions and computers and other electronics, radioactive material, explosives, gas cylinders unless they're empty and delivered separately, appliances that still hold Freon, vehicles and major vehicle parts, infectious waste, and yard waste. Water-based paint has to be dried out solid before it can go in.
Drums, barrels, and buckets are only accepted with the lids off and the insides cleaned out, so plan on that for a shop or garage cleanout.
Yard waste needs its own route. The City collects grass, leaves, and branches up to two inches thick separately at the curb, and the landfill won't take it mixed in with construction debris.
If any item on your list looks borderline, ask your account manager before it goes in the container.