What happened is that during the 50s and much of the 60s Miami still lived in an age of relative innocence with very little violent crime. I remember Ralph Renick going into a fury every so often about the illegal sale of Bolitos (non-government lottery tickets) but that was about it. Things changed swiftly after the Mariel boatlift in 1980. You can see some of that in Scarface where blissful Miami Beach went into a steep violent crime wave. Also most of the retirees living there reached the end of their natural lifespans with few to replace them.
Anyway, the Mariel boatlift people were eventually mostly gone (Read Elmore Leonard for a sense of what was going on during that era). And the TV show "Miami Vice" brought back a lot of tourism (especially from Europe) that was lost before. Now when you go to the hotels in Miami Beach, most of the visitors are from South America.
In many ways, Miami has been revitalized so that is a positive. However, that age of 1950s innocence in which slot machines and risque "Girly Show" signs were at the forefront of a "crime wave" is Gone With The Wind. Check out "Surfside 6" shows to get a bit of a feel of old innocent Miami.
Posting this from Wynwood. It feels like Mexico here and nobody speaks English.