But its effects are still being debated around the state, even as thousands of Floridians prepare their applications for the new concealed-weapons permit. David Register, Director of Licensing in the Secretary of State's office, said more than 130,000 permits are expected to be issued in the year that begins Oct. 1. That figure, said John J. Katon, president of the Tamiami Gun Shop in Miami, ''is just a tip of the iceberg.''

The gun shop offers a two-hour firearms course that helps applicants meet the requirements for the concealed-weapon permit. In addition to taking a safety course, applicants must pay $146 and submit to a fingerprint check. Anyone at least 21 years old with no felony convictions who has lived in the state for at least six months is eligible.

By contrast, Dade County gave concealed-weapons permit only to applicants who had a valid reason for needing it and had passed a backgound check and a firing-range test. The county permit fee was about triple the state fee. Ease of Application

Rodolfo Padron, a business executive who has a Dade County license, plans to apply for the state permit even though he opposes the new law. ''I had to go through a thorough checkup before they gave me my permit and now almost everybody will be able to legally carry a gun,'' said Mr. Padron, who carries a gun when he makes cash deposits of business receipts.

Michael Freire, general manager of Tamiami Gun Shop, said the simplicity of the new application has attracted many customers to the required safety course. ''Everybody who is taking the course says that the law offers an easy way to obtain the license to carry a gun and the opportunity to defend oneself against criminals,'' Mr. Freire said.

One issue - crime - shapes arguments on both sides. According to figures compiled by the Federal Bureau of Investigation, Florida's crime rate has been among the highest in the nation for years. In 1985, the bureau said, Florida had 7,574 violent crimes per 100,000 residents. Last year the figure was 8,228. By comparison, New York State had 5,588 violent crimes per 100,000 residents in 1985 and 5,776 in 1986, the bureau reported. 'It Was About Time'

''It was about time for Florida to have such a law,'' said Richard M. Manning, a National Rifle Association official who pushed for the legislation.