I'm new to diving, but probably an 'advanced beginner' when it comes to understanding treasure hunting in Florida. As Dennis alluded to, the state of things as they exist today is enough to raise the Libertarian in anyone...
Treasure hunting in Florida- and particularly historic maritime salvage- has long been a part of the states soul and it went on relatively unimpeded until Fisher found the Atocha, 'beat city hall' via his Supreme Court victory and inspired the passage of laws on the Federal Level that undid Federal maritime arrest in many waters and threw back authority to the states, effectively wrapping the tentacles of state bureaucrats around the whole show.
Maritime Treasure Salvage in Florida is a 'thing' unto itself... As best I understand it (and I'm sure there are people here who know the minutiae involved and will correct me if I'm wrong...), you first must obtain an "exploration" permit, then after a nightmare of bureaucracy, apply for the mythical salvage permit, which they almost never issue anymore.
There are a number of grandfathered leases in Florida where Treasure Hunting is still permitted- for example, the original Fisher leases, which I believe still operate on a 20%/40%/40% split (20% to the state, 40% to the lessor and 40% to the treasure hunter)- again, I'm speaking in approximations here.
In various state parks and beaches, you're allowed to metal detect from the toe of the dune to the tide line. You're not allowed to detect in the water with an immersible unit. Same goes for treasure areas that are governed by an active lease. You might be able to metal detect on the beach, but bring that Sea Hunter knee deep into the water of Wabasso Beach and you're in no-no land...
As far as other forms of underwater treasure hunting in Florida, I do know they take a hard line pertaining to anything over 100 years old. Up until 2004 (I think) the state had an "Isolated Finds" program, where people who occasionally found stuff could fill out a form and if it wasn't of any real historic import, they could keep it. They discontinued this due to lack of utilization.
If you're interested in fossils, you can get a permit from the state to collect them on state lands, which I do believe also applies to waterways.
FLMNH - Vertebrate Paleontology - Florida Fossil Permits
At a minimum, this should be enough to ward off a bored cop with nothing better to do than hassle you for diving and looking.
As an aside, there are green chutes of an active movement amongst the treasure hunting community to start undoing some of this bull**** and allowing people to chase their rainbows, as they please... Stay tuned.