I think this topic is trying to divide in half.
Some people are talking about numbers balance, and other people are talking about mechanical effects for dwarves with scarred or mutilated organs.
These are closely related, but they aren't the same thing.
The pain from a ruptured appendix will put most people out like a light, but I know people (scarily tough people) who have walked into a clinic hours after the fact. We all know people or stories like this, of normally crippling injuries being disregarded through sheer fortitude, but the fact that these stories strike us as odd is telling; it's possible to do that, but it's pretty rare. It isn't that ruptured appendixes should automatically knock people out all the time, they just aren't doing it often enough to average toughness people.
For the numerical balance, I'd like to see a wider range of possible bleeding values, and more drawbacks to major bleeding. Minor cuts might bleed a little too much, but arterial cuts don't bring down average strength opponents fast enough. Loosing blood can cause shock and pain, in addition to the shock and pain from wounds, which is currently too weak to stop even a wussy and weak-minded fighter. Pain is pretty new, all things considered, so Toady's reluctance to make it very powerful is understandable.
I'd like to see bleeding close to the brain (say a slashed out throat) make it harder to stay conscious, but this is likely a bias based on my own fighting style and inconsistent blood pressure.
Organ injuries are where we started, and I have a bit interest in that. It has two times when it should really take center stage: during recovery, and post recovery. Combat should be about shock, bleeding, and disabled limbs in most cases, with organ strikes or slit throats being valuable opportunity shots, instead of the whole story.
It adds a lot of verisimilitude to the post-battle mini-game, e.g. patching up the wounded.
Without modern medicine, crushing injuries to the abdomen are far deadlier than strait-up evisceration, or gut stabbing (which, as others have already said, don't do much right away, but can kill you later), because blood clotting medicines and surgery will be much less effective in the period (they are still among the deadliest industrial accidents, as you can't simply stitch up something crushed into jelly).
A badly crushed liver is a very risky proposition, even now, as moving the patient improperly can cause a sudden rush of bleeding that kills in minutes. The thing that makes these scary is that a patient can be stable and recovering for a few days, and then suddenly start bleeding again and die before anyone can react. It isn't common, but it happens more than often enough. In game, this keeps things unpredictable for the player, who may or may not get his warrior back after a few months.
I have mixed feelings about post recovery effects. There's a lot of potential to get bogged down in trivial simulation stuff, like the effects of digesting nuts without a gull bladder, and I don't think that's a good use of computing power at this juncture. The focus should be on things that can be generalized (so toady can re-use code, and creatures with wierd physiology are accounted for), or things that have really major effects.
Visible scars, due to their social effects, are the most interesting lasting injuries, and it is right and natural that they see more attention than internal scarring. We've already got some good effects for the major stuff here, like losing a limb or all of your eyes. I will never complain that scars are getting too much attention, at the expense of post recovery organ effects.
Joint injuries are pretty common and have intuitive effects. Everybody knows somebody with a bad back, elbow or knee, so the effects will make sense. A minor loss of agility, pain during poor weather, sluggishness before warming up, penalties to actions involving the effected limb, etc. Joint injuries are a major fear for athletes, craftsmen and fighters alike, as they threaten to impair their performance or even end their careers. Mis-set or shattered bones could have a similar effect.
Damage to the immune system cold be generalized as a simple stat penalty, so it's probably pretty easy to do. A dwarf that takes more sick days is a pain, but it's not the end of the world unless he works in a miasma factory.
Things like this, that hit a lot of organs at once, are what I want to see. Special functions for every jibbly and splanch seems like a good way to waste a lot of Toady's time for no real purpose, especially when that sort of stuff won't be useful to modders making really weird creatures.