Here is a massive set of docs on it:
http://fac.dos.state.fl.us/faconline/chapter68.pdf
A summary someone posted:
For Florida spearfishermen:
In Florida state waters, it is illegal to recreationally spearfish on a rebreather. Florida commercial regulations also prohibit the use of a rebreather for tropical collection.
In the South Atlantic EEZ (i.e., federal waters > 3 nm from North Carolina/Virginia border to a line extending south near the Dry Tortugas, Florida) it is illegal to use a rebreather to spearfish those species in the Snapper-Grouper FMP (i.e., snappers, groupers, triggerfish, porgys, jacks, tilefish, grunts, spadefish, hogfish, and sea bass).
Other target species like dolphin, wahoo, mackerel, cobia, etc. are legal to spear in the South Atlantic EEZ on a rebreather.
In the Gulf of Mexico EEZ (i.e., > 9 nm off Florida; either 3 or 9 nm seaward of other Gulf states), there are no prohibitions specific to the use of a rebreather.
Regardless of the regulations applicable to spearfishing and rebreathers, the next question one needs to ask is if one's diving would benefit from a rebreather - beyond that of a cost savings. Fast descents/ascents on rebreathers are more problematic compared to open circuit; if you are doing short/fast, deep bounce dives, these might not be what you are looking for due to the need to establish your setpoint, buoyancy issues on ascent, etc. You have to be vigilant when using these, make sure it is operating as it should, as the repercussions can be severe. Unless you want to be risky and are planning to follow an alpinist approach, you will still need to carry an open-circuit bailout tank (e.g., AL40 typically slung under your arm), so the overall package will be less streamlined and bulkier than a single steel tank with pony bottle. Depending on what unit you are considering, you will also have more clutter on your chest. Your vision will also be a tad more limited, as the loop doesn't allow you to swing your head as freely or as widely compared to open circuit. Extra protection of the unit on the boat deck will also be required, as a spear tip or spine from a fish sliding across the deck can give you a big headache. Also keep in mind that there will be no bubbles to disuade sharks from running in on you out of nowhere (i.e., they might not circle or take time to check you out), so you better be good with your PPD and have eyes in the back of your head
These are just a couple issues that are apparent.