Most building and household debris is fine to load. The limits come from Ohio's landfill rules and from the facility that takes the load.
The Ohio EPA says trash landfills can't take hazardous waste, PCB waste, bulk liquids or wastes with free liquids, scrap tires, or yard waste. That means leaves, grass, and brush should stay out of a general debris container, and tires need to be handled on their own.
Standard exclusions also apply. Keep paint, solvents, fuel, and asbestos out of the dumpster.
The county's transfer station runs residential drop-offs for electronics, household hazardous waste, oil and antifreeze, yard waste, appliances, and scrap tires. Those programs are a good home for items that don't belong in your container.
If you aren't sure about something, ask your account manager before it goes in.