Most household and jobsite debris loads without trouble. The limits come from Ohio law and from the City's own rules.
Ohio bars lead-acid batteries, the kind in cars, boats, and mowers, from solid waste landfills. You cannot mix one with solid waste or leave one at a disposal facility, and the retailer that sells you a new battery has to take the old one back.
Hazardous household material is out of the container as well. The City's list covers acids and alkalines, aerosols, antifreeze, bleach, cleaners, polishes, disinfectants, pesticides, paint thinner, turpentine, varnish stripper, and oil-based paint, and it says plainly not to put any of it with regular trash. Lithium ion and other rechargeable batteries should never go in garbage or recycling because they start fires.
Latex paint is the one exception worth knowing. Once it is fully dried out, with cat litter or a drying agent mixed in, the City treats it as ordinary trash.
Asbestos, propane tanks, fluorescent bulbs, medical waste, and fire extinguishers all need their own handling. Mention anything unusual to your account manager before it goes in the container.