Although the dress code during the day or early evening in South Beach is "anything goes" casual, most clubs have fairly strict dress codes. And beyond that, most clubs actually have doormen (or doorwomen) whose job it is to select only the rich, famous, beautiful, and hip to let in. The most popular clubs will have people waiting to get in, standing in line on the sidewalk by prime time (midnight and after), held "in check" by velvet ropes on upright stands (similar to what lines going into movie theaters have). Those people may stand for a long time, and in fact may not necessarily get in. Dressing appropriately will help your chances of getting in.
For women, the words are "tight, sexy, sophisticated, and black". Black is by far the color of choice for South Beach nights for both men and women. Skirts (often miniskirts), tanks tops, and high heel shoes (or high heel dress sandals) are quite popular. And a modern interpretation of the "little black dress" is popular, as are fashionable pants (again, "tight" seems to always be the word describing South Beach female fashion). In addition to black, the color white is often seen (such as a black skirt and a white top). In summary, women stand the best chance of getting into the clubs if they are dressed (and made up) sexy, but with the hip sophistication of a fashion model. In reality, however, if a woman is attractive, she stands a good chance of getting into a club, as the clubs like the reputation of being a draw for "the beautiful women".
For men's clothing, you can rule out shorts, sandals, T-shirts that have any sayings or logos on them, and caps (e.g. baseball caps). And anything hinting of a "grunge look" will typically ensure you don't get into the top clubs. For men, the goal is to look hip, sophisticated, and wealthy. As with women, black is definitely the color of choice for the South Beach night scene. Nice black slacks, and a body-conscious black shirt, topped off by expensive black shoes (all with a modern hip flair) are perhaps the best bet. If the weather isn't too warm to prohibit it, a sport coat (black, or something suitably subtle and sophisticated), or a suit are also excellent (in South Beach, suits are often not worn with ties...an elegant mock tee underneath is common). And for men, too much jewelry (neck chains, etc.) will generally not help your chances of getting into the clubs.
It's probably worth mentioning that having roughly an equal number of women and men in a party (or at least some women) also helps your chances of getting in. Clubs are often reluctant to have lots of "leering men" standing around inside.
So, dress your sophisticated sexy best, and hope you look beautiful, rich, and hip enough to get in and enjoy the great South Beach clubs.