In the movie In Time, people have modified genes so that they stop aging at 25. Does that also curb disease, or can they die from any sort of disease?
It's never explicitly confirmed, but the strongest evidence is during the Poker game after Will arrives in New Greenwich.
Philippe Weis says: "When you've been 25 for 85 years, like I have, knowing only a random act of violence can take your life,.."
This certainly seems to imply that disease has been eliminated.
No-one appears unhealthy, not even the 60-year-old prostitute in the screen when the Timekeepers find Henry Hamilton.
Since they have the technology to halt biological aging at 25 (in everyone, so probably genetic engineering that's dominant in everyone's DNA), eliminating disease would be the easy part.
People in the world of "In Time" do indeed suffer from diseases, however medicine seems to have advanced to the point that even rapidly fatal diseases are able to be kept at bay with trivial ease.
From the original script (back when the film was I'mMortal)
A WOMAN argues with a VENDOR over the cost of medicine - shows him her clock with four days on it.
WOMAN #1: A week?! I only got four days. What good's the medicine, if buying it kills me?
VENDOR: [unsympathetic shrug] So let the disease kill you.