Most construction and cleanout debris loads without a problem. The limits come from Florida rules and from what the county landfill will take at the scale.
Florida lets you dispose of up to 25 waste tires a month without a permit, and anyone with more than that has to register with the state environmental agency, so tires are worth keeping separate and declaring.
Asbestos has a strict route here. The county only accepts it Monday through Friday until 3 p.m., with a waste shipment record completed and the drop-off booked at least 24 hours ahead, so it never rides loose in a container. Drilling and boring mud, slurry and bentonite are refused outright. Soils, fill dirt, dredge material, street sweeping grit and sludge all need approval before they arrive.
Hazardous material stays out everywhere: paint, solvents, fuel, motor oil, pesticides, pool chemicals and car batteries. The county runs chemical collection centers on Bee Ridge Road in Sarasota and South Jackson Road in Venice for those. Ask your account manager about anything you are unsure of.