As a criminal defense attorney, sadly, I have found it is all too easy for individuals to be arrested. If this was your first arrest and it qualifies under Florida law, you may be able to have your record expunged (destroyed) or sealed. You should contact a criminal defense attorney who practices in Palm Beach County to consult about your case.
You can sue, but then you have the burden of proving that the police arrested you maliciously, or that the persons who reported you did so in bad faith, etc. It is a very difficult thing to work through.
For example: Say a devilishly handsome, tall, and suave criminal named James Davis has a warrant out for his arrest. I am out cruising the town in my ultra hot 92 Elderado when I am pulled over. The police officer checks, and then arrests me because I fit the description. Even though my legal name is Jimmy, that is a common nickname for James. I am devilishly handsome, tall, and suave. Any officer who arrested me would probably have a good faith defense that I was that criminal and the arrest was thought to be valid.
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You can sue but it's a difficult case to prove. The state also has sovereign immunity, limiting recovery in most instances anyway. Indeed, it's an unfortunate system. The government makes mistakes pretty regularly and I think you're right, if the bar was lowered to sue them, they'd be more careful. On the other hand, if the bar was lowered to sue them, it would probably throw an enormous wrench into the system, leading to a system where we spend more tax dollars while crime rates go up. Not saying that's my position, but that's the argument.