Placenta problems can happen at any time (me for example) but the further you go overdue the higher your risks are for these types of problems. I also have a friend who had her dates messed up and when her son was born he was only 5lbs3oz (I believe) he was so dry skinned, real bad blood sugar levels, he was so small and sick looking... he was in the NICU for a few nights due to this and the doctor's told my friend her amniotic fluids were so low that her waters didn't break and the doctor's didn't break them (dry dry birth) and her placenta was very aged. She was on the verge of having a possible placental abruption which can lead to death for mother and baby. I only lost my son, I survived but it was a miracle I am even here. I was only 37 weeks when mine detached, due to high blood pressure, not being over due. My son passed 8 hours after delivery via emergency c-section, blood transfusions for him and myself etc...
I highly recommend not letting yourself go over due if you can help it and really don't push to go even further than your doctor advises. I personally don't think it's worth the risks hun. So many things can happen... not like it happens every time but they can... and that is enough for me.