You could mess around with IT systems and change data. Goverment funded IT projects are usually terribly done. See tax credits as an example.
Depending on how the information is used (if it's shared for example), insurance companies could refuse to do life insurance, private etc.. if you're predisposed genetically to certain health issues.
Also, DNA can be left all over the place. If someone was murdered in my room say, my DNA would be all over the place, (well my hair or something at any rate). Not great. DNA in that case wouldn't be helpful exactly would it.
If a woman cried rape but it was actually consentual sex. The blokes DNA may be there but what use would it be in a case like that other than to make him look guilty?
Also, I'm sure there's some rules/laws about admitting/using DNA evidence in court anyway which would probably make the whole thing redundant. (That's the bit the sciencey guys know more about than me).
So yeah... Don't entirely see how it'd be useful.
DNA is not 100% full proof is basically what I'm getting at.