My daughter was falsely arrested by the San Diego Sheriff' Dept. due to a clerical error. ( and jailed)
Her bail was $5000 which cost her $500.
She was cuffed in front of neighbors who most do not know it was an error. Reputation ?????
They admitted the mistake and dropped charges.
I think they owe her more than an apology.
If the error is a result of a policy or custom then you might have a case otherwise you're pretty much out of luck if it was a simple mistake.