Fun fact, they can sometimes narrow down crime scene DNA to just a single person by having enough partial matches from their (potentially distant) relatives. I can't remember which DNA database was used, but some cases were solved this way, IIRC it introduced a bunch of legal questions about if you can search a database in that way.
There have also been a number of false positives because many believe that DNA is infallible. What people tend to forget is that DNA tests used by law enforcement is only using a very small subset of DNA markers. This mean that if you're already in a DNA database you can get an unpleasant knock on the door just because you have 10 DNA markers in common with some random criminal.
Danish police only upgraded from 10 DNA markers to 16 in 2021, forcing them to review 12.000 cases and redoing the DNA test. Resulting in at least one person having the sentence reversed. No word on how many was falsely suspected, but I assume more than a few.
I think this was the article that talked about this (apologies for the paywall): https://www.nytimes.com/2021/12/27/magazine/dna-test-crime-i...