Depends on what the record is. Some records can be sealed or expunged. He needs to consult with an attorney and someone that specializes in working with the board to admits medical professionals in the state.
Personally I doubt that any juvenile misdemeanor will disqualify someone from becoming licensed after growing up to successfully complete medical school, but, then again, I don't make the rules.
Everything that you ever wanted to know about acquiring a medical license in the State of Florida can be found at the following 2 websites:
First, second and third: No attorney-client relationship exists by virtue of any Q&A with Michael A. Haber, Esq. on Avvo. Fourth: Anything that you post on Avvo (or on similar sites) or on any social media is by its nature public. It is essentially an admission / confession and can be introduced into evidence as a statement against your interest in a subsequent legal proceeding. Once posted you lose any reasonable expectation of privacy, so, as this is an open forum (with no privilege attached), please be extra careful when considering what to post online (forewarned is forearmed.)
Keep in mind that sealing and/or expunging a criminal record may not prevent him from having to reveal the existence of the past criminal issue. Some applications for employment and licensure may ask about the existence of past crimes, even if expunged/sealed, and may require a signature under oath affirming that all information has been disclosed. Concealing the sealing/expunction can be grounds for denial or termination of licensure or employment. That being said, I doubt that a misdemeanor will prevent your son from obtaining licensure. I personally know many professionals, both doctors and lawyers, with criminal histories more severe than a misdemeanor as a juvenile. I would read as much as possible on the moral/ethical considerations for medical licensure to evaluate his chances.