I think that people are using “medical mistake” in several different ways.
First there is gross error that caused three deaths at Duke (one, the patient; two, the person who should have got the first heart that she got; third, the person who would otherwise have got the <i>second</i> heart she got). Ok, there is some double counting there, but anyway the mistake caused two deaths. I suspect that, while the medical profession is far from perfect, this kind of error is rare.
The second kind is what might be called the error of hubris. The doctor gets it in his mind that the patient suffers from X when the actual condition is Y and treats X and the patient dies of Y. Or suffers serious injury. This is the statistic that I would really like to know since it tells you how important it is to get a second opinion. And this, like the first kind, is subject to amelioration. But unlike the first kind, it is probably much more common than we know. Given doctor’s god-complex, it is hard to convince them that they may be wrong (not all doctors, but all too many).
Finally, there is a third category of the doctor who didn’t do every possible test and thereby missed something. This is the most complicated and difficult area of all, since there are valid reasons for not doing every possible test. Tests cost money and while we might not like to admit it, money does matter since money spent here cannot be spent there. Just as a heart transplanted here cannot be transplanted there. Tests are often invasive, often unpleasant, sometimes carry a not infignificant risk in themselves (I believe I have read that an angiogram, just a diagnostic procedure, has a 1% chance of death). And many tests simply give far too many false positives that lead to really expensive and dangerous followups.
Here is a thought experiment on the latter point. Suppose there is a condition that is so rare that only one person in a million suffers from it. Suppose there is a screening test that never has a false negative, but has 1% false positives. If you screen 1,000,001 people, you will get 10,001 positive responses (expected value) of which 10,000 are false and one true. That is 10,001 patients on whom, let us suppose, expensive and possibly dangerous followups are now required. Let us imagine that 2 of those 10,001 people die as a result of the further tests. You now have killed two people and spent untold amounts of money to save one life. On the other hand, if you don’t perform that screening, then some high priced lawyer can find some doctor somewhere who can be paid to testify that the screening test should have been administered that would have saved his client’s life.
There, and I haven’t ever mentioned g__s.