A lot of Dade County is in the Everglades National Park, and as such is under the auspices of the Federal Government. In most states, the county would still have jurisdiction there, but municipal government does not. I'm not sure if that is the case in Florida.
There are also areas of protected seashore that are not in the municipal jurisdiction. According to the Miami-Dade Website
there is police and fire protection in these areas. There may be questions of jurisdictional boundaries arising from the combining of the City of Miami and the Dade County Public Safety Functions. Miami-Dade county is a home-rule district, so their jurisdictional situation will differ from the rest of the State.