The answer to this question is going to depend on your contract with your landlord as well as the landlord/tenant laws existing in your state. I would recommend finding an attorney in FL who practices in the area of landlord/tenant law so he or she can help you determine whether you might have a claim against your landlord.
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While it sounds like the real estate company could be liable to you for their misrepresentations, the real difficulty will be proving damages. Damages appear to be minor since you have been able to live in the apartment, you have not received any personal injuries as a result of the code violations, and you can find another place to rent. Are you able to rent another apartment for roughly the same amount? If you decide to sue, you might try to ask the Court for any difference in rent, along with your moving expenses. In Florida, you can bring a small claims action for a claim in the amount of $5,000 or less, which might be an option.