The question is, how much of it was due to doctors with poor handwriting???

Since I am directly involved with this I'd say, such errors are always there. More importantly it's about moving demand away from capacity, it does not replace secretarial function. Given all the fuss you would think it was

I had to type these things as well for 2 weeks as a holiday job.

There are a lot of problems here:
(everything was on tape, and had to be typed out)

1/ doctors don't articulate good (some are so bad nobody knows even not themselves)
2/ it gets typed by people who don't understand it and therefore don't really know if what they are typing makes sense
2bis/ they let student IT type it, without any medical background

solutions? let the doctors type it :p but i guess that won't happen soon, so no real solution i guess

The solution, David and others, is to have qualified medical language specialists do the work, either by keyboarding the reports directly or by editing a pregenerated speech recognition document. Trained medical transcriptionists and medical editors do understand the medical dictation they are transcribing. I often can predict what sentence a dictator will say next based on my 18 years of experience doing this job for dozens of acute care hospitals in the United States.