Everyday construction and household debris is acceptable. The exclusions come from Florida's disposal rules and from the city's own container rules.
Under Florida law, lead-acid batteries are kept out of landfills and out of waste-to-energy plants, used oil is kept out of the waste stream, yard trash is kept out of lined landfills, and large appliances are handled separately. Those rules apply to your container as much as to a curbside cart.
The city adds its own prohibitions. Hazardous waste must not go into any container the city's collector services, no container may be filled so that the lid will not close, undrained liquids are not accepted, and burying or burning waste inside the city limits is not allowed.
Hazardous waste, liquids, paint, solvents, fuel and asbestos stay out of a standard container as a matter of course.
Heavy inert material such as concrete, tile and rubble is best kept as its own load. Mixed in with lighter debris it pushes the weight up and can change how the load is classified on arrival.
If an item is borderline, ask your account manager before it goes over the rail.