Most remodeling debris and cleanout junk is fine. The limits come from Florida's landfill rules and from what Miami-Dade County's facilities accept.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The City also asks residents to keep chemicals, tires, paint, and car parts out of its own bulk drop-off containers, and the same items should stay out of yours.
Asbestos has its own path. Miami-Dade County takes it only at its south landfill, and only with advance approval from a County regulatory office. If your building may contain asbestos, sort that out before demolition starts.
Hurricane cleanup and yard debris are common here. Palm fronds, branches, and yard trash are accepted at the county's trash landfill, but keep them free of paint cans and chemicals.
If you're unsure about an item, ask your account manager before you load it.