I found the following on wiki, and am wondering if anyone else knows more on this. Is it strictly a gun show thing, or does it apply to all private sales?
Florida law allows private firearm sales between residents without requiring any processing through an FFL. Florida law also permits larger municipalities to elect to require a concealed carry permit for a buyer to purchase a gun at a gun show from another private individual without any delay, but in practice, this applies only to a few of the largest municipalities (Miami, Orlando, etc.) where it has been invoked.