Most household junk and building debris is fine to load. The limits come from Ohio's landfill rules and from the facility that takes your load.
The Ohio Environmental Protection Agency says municipal landfills can't accept hazardous waste, PCB waste, bulk liquids, scrap tires or yard waste. That means grass, leaves and old tires should stay out of a mixed load.
Beyond that, hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The City's own Sanitation Department doesn't allow hazardous waste in any container either, and it points residents to Summit ReWorks, the county's waste agency, for household hazardous waste.
Appliances and car batteries are best kept separate and mentioned when you book.
If you have something you're unsure about, ask your account manager before it goes in.