I think continuity of care is one of the biggest risk factors. Being with the same MW/obgyn throughout means that they will know your health, your risk factors, you etc. and that has to help.
With DS1, I had him in the UK, and while I can't actually fault the MWs and the delivery team, I had a near miss myself post-natally because the registrar who wrote up my anti-coagulant gave me highly ambiguous instructions, which meant I ended up taking a triple dose of warfarin instead of the correct dose. Luckily for me I wasn't bleeding heavily! IF the haematology consultant had done that write up, the near miss would never have happened but the obgyn reg didn't really understand the situation. I did report it because it could have been very dangerous (wasn't, in my case) and because the reg needed to learn from it.
Had DS2 in Australia. 5 years older, higher risk pg, decided to go with a private obgyn because that way I wouldn't have to KEEP telling them about the clotting condition, the other things I had going on etc. Yes I had to pay for his services, but it was the best thing I did for our health.
As proven when I had my appendix out last year (in Australia) - I kept asking them when I was getting more anti-coagulant, and where they prescribing some for me to take home, but they kept saying no because SOMEHOW, they were failing to read the bit that said "Thrombotic condition" which means that, post-op, I should always be given anti-coagulants for 5-7 days. I had to go to my GP as soon as I could (out of hospital on the Sunday, GP on the monday) to get this sorted because I didn't feel like running the risk of a DVT or PE due to lack of anti-coagulant. I reported this when I went to my post-op follow up as well.
SO MUCH of the "near miss" situation is failure to read the notes, be clear about the situation, follow up on basic protocols - some of it is due to lack of time, tiredness etc. but sometimes it's down to lack of due diligence.
I used to work in hospital labs and have seen that in action myself too. Wrongly labelled blood, for e.g., because the doctor taking it was carrying the wrong notes and neglected to ask the patient their name/d.o.b etc for clarity. As it happened, they had 2 patients with very similar names in the same ward - but different dates of birth, so ASKING them for their 3 points of ID would have differentiated. Luckily for the patients, they had different blood groups and were already in our system, or it could have been very nasty indeed.