In terms of medical data the amount of leakage is somewhat limited by the nature of DNA, e.g because you get a random mix you can't conclude anything about parents, etc medical status.
By far the biggest practical knock-on effect is if you match someone who's doesn't know their parentage (adoption/illegitimate children/etc) who can figure out their parentage as a result of that match.
Familial DNA crime searches are probably the next biggest, but they're still very rare at the moment and many of the DNA platforms don't allow them (GEDMatch was one of the few that do).
By far the biggest practical knock-on effect is if you match someone who's doesn't know their parentage (adoption/illegitimate children/etc) who can figure out their parentage as a result of that match.
Familial DNA crime searches are probably the next biggest, but they're still very rare at the moment and many of the DNA platforms don't allow them (GEDMatch was one of the few that do).