Damages require proof. Unless they can show they lost something because of the mistake, then there are no damages.
However, not all US states allow all types of damage claims and/or have special rules or higher burdens of proof related to those types of claims.
Generally speaking though, it is incorrect to say that somebody must show that they have had actual, monetary damages in order to be successful in a defamation lawsuit.
This overview from the Legal Information Institute (Cornell Law School) has some helpful info: https://www.law.cornell.edu/wex/defamation
You're basing your understanding of slander/libel on US laws I presume? If that person lives in Europe, generally, the bar for a successful lawsuit is __extremly low__ , it only requires the information to be blatantly false, there is no need to demonstrate the victim incurred any damages.
However if we are talking about monetary damages, those require hard proof of the damages and even then it is unlikely that they will have to pay all damages. Most lawyers I talk to usually recommend against suing for monetary damages.
Well, you can ask for "moral damages" and the judge might grant you these damages in Europe, I'm pretty sure the bar is also quite low for these. If you are from US keep in mind that million dollars damage verdicts are rather uncommon in Europe for individuals. That's the trade off. So judges might grant the suing party "moral damages" much more easily as a counter part. Of course it varies from country to country. IANAL.