Most remodeling and cleanout debris is fine. The limits come from Florida's landfill rules and from what the Broward County Landfill will take.
The county landfill is a Class III site. It only takes bulk waste, yard trash, and construction debris from inside Broward County. It turns away household garbage, hazardous waste, medical waste, car batteries, used oil, and anything with PCBs. So food scraps and bagged kitchen trash need to stay out of your container.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
Tires are taken but priced by the ton on their own. For paint, chemicals, and electronics, Broward County runs residential drop-off centers on Saturdays for people in participating cities.
When you're unsure about an item, ask your account manager before you load it.