I would worry about coast guards mostly. For some reason they got pretty anal on me lately.
They consider SUP a boat so you have to have a light, whistle and a life jacket on board. I use Belt Pack Inflatable Life Jacket (Onyx Type V M24) and the smallest waterproof light and whistle that I put in the pocket of the pack. [It's not a bad idea to have all this stuff anyways, if you're going into the open sea].
Since it's a "boat" I would avoid swim zones.
Surfers... They are hostile to anything that gets in a way to catch a wave. The fact that you can catch waves way earlier drives them nuts even more
. But you can always choose a spot that is not good for them but is perfect for you. If they still come to you and give you a hard time after that - use the paddle (as a long durable stick) for further explanations
.
Not sure about any restrictions on the beach... never encountered any...
All the above applies to Tampa Bay (intercoastal waters and the Gulf)... but I think it is the same in Miami area.