Just that it is very unlikely that you could infer the clinical manifestation of a heart condition just from DNA alone...
If they're just comparing the DNA that was left behind at the police station to DNA they found at a crime scene, I don't see any issue.
IMHO the EFF have chosen the wrong case to fight here.
Therefore, if we made a rule that evidence that ties you to a crime scene (such as fingerprints) can be collected without a warrant, but evidence that identifies you as the perpetrator needs a warrant, couldn't the police simply collect the DNA from the chair without a warrant, and only use the DNA from that sample to tie him the crime scene?
Then, once he's tied to the crime scene, that could be used to justify a warrant to collect a direct DNA sample directly from him, and then they could use that second sample to identify him as the perpetrator?
And if the rapist in this case was questioned as a subject, the police could have gotten a warrant for the DNA anyway.
This typically happens with civil rights cases, and it's worth noting that there are certain legal groups that are better at it than others -- the Second Amendment Foundation is exceptional, and it's a large part of why their win record is so good.
A fingerprint however, if found in public and considered fair game tells you one thing - that you were there, or someone reasonably competent in lifting and transferring fingerprints has a copy of your fingerprint and is attempting to put you in the spotlight. It doesn't tell the discoverer of your print anything further about you.
Your fingerprints don't tell me anything about your mother, you medical history or future, or hers.
When someone takes your DNA, they search your entire family.