Most building and household debris is fine. The limits come from Florida's landfill laws and from how local facilities sort what they take.
Florida law keeps a few items out of landfills entirely. Lead-acid batteries, like car batteries, and used motor oil are two of them. Large appliances, which the state calls white goods, are on the list too. Yard trash also can't go into the lined landfills that take household garbage.
The usual exclusions apply as well. Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
Sorting matters in Tallahassee. The City treats bricks, concrete, lumber, drywall, plumbing fixtures, and shingles as construction debris that shouldn't be mixed with garbage. Tires are charged by the ton at the county, so keep them out or mention them when you book. Leon County takes household hazardous waste from residents at its Apalachee Parkway site.
If you're not sure about an item, ask your account manager before you load it.