I'm going to answer this tangentially, as a semi-frame challenge, and hope this gives the inspiration.
I would start with what technologies/capabilities you want your Sci-Fi Medicine to have - and that will largely dictate what will still be an issue and what won't.
Also to add - just because something is capable of being done, doesn't always mean it's reasonable to do on a mass scale.
So let's start:
Artificially growing organic replacement body parts
This is a big one for all your bog standard trauma issues - if you have the ability to grow a new leg or new organ, many of of your injuries can be mitigated by simply replacing the damaged part.
If your world has the ability to reliably edit Genes, then all your genetic ailments could be mitigated - whether that's Down syndrome or simply male-pattern baldness.
Rogue cells therapy
Think of all your cancers, Auto-Immune diseases etc. where the bodies own cells are doing something that they shouldn't be - if you have the ability to edit or otherwise target these cells (Nano-bots, special space medicine, targetted inhibitors - you name it) - then you can remove all of these from your world.
This is a biggie - Spinal injuries, brain injuries (we'll get to that in a min) and other issues where there's been significant damage to nerves, nerve endings and other bits - if you can repair these, you can rule those out...
However - you are at liberty to dictate the complexity, it stands to reason that repairing the nerve endings in say the finger is orders of magnitude far easier than repairing TBI (Traumatic Brain Injury) and so you can have that as your limiting factor.
This is probably the most important one - can someone be put into Stasis or suspended animation or Cryosleep or other scenario where someone has suffered a massive and sudden injury that would result in death in minutes or seconds - can they paused until they can get to the appropriate medical centre?
Fixing the physical body and fixing a broken mind are not the same thing - and you can have a lot of fun with this. You could make an argument that advances in medical technology has created a whole host of mental problems because the Human mind evolved for small, tribal groups that regularly faced death, disease and war - Just look at the rise of Mental Health issues in the west, when compared to other civilizations.
One can even argue that no technological solution will fix this problem - so that's always a lot of fun.
Your Sci-Fi universe can always find ways to be deadly - I'm an Avid WH40K fan and the Space Marines are written to have multiple artificial implants to increase blood clotting, filter out poisons etc. to make them nigh un-killable by regular means - but in universe, the threats out there are so bad and terrible that they are able to be killed.
Things like vaporization from a Plasma weapon - no amount of Medical tech is likely to repair that.