I remember one classic one is the "no coffee when pregnant", the study says this causes problems, the test was performed on rats and by feeding them coffee in the amount of 3/4 of their body weight. We can agree that with this amount, it's reasonable it could cause problems. Very different from one cup of coffee though.
The other study that was done is about Amniocentesis, this one is more interesting the chance of miscarriage is considered 0.1% but this was before the operation was performed with a live ultrasound to look at the needle while performing it, which (probably) makes a big difference. Before, doctors performed an ultrasound and then went in blind.
There was also a serious bias towards a certain type of population. But of course doctors don't bring this up at all.
Last thing is sids, it's a terrible type of diagnosis that pushes parents against the instinct of sleeping with their children, even though this is commonly done in non-western cultures and can save a lot of pain to the parents and give a lot of security to the child. Do your research though, medical community reports risks and I'm no doctor, just a dad who read a few books.
Glad my children are healthy. Every time I read about some illness for children I feel an incredible weight on my heart