Placenta usually starts showing signs of getting old once a singleton pregnancy reaches 40 weeks and twin pregnancy 38 weeks. What it means is that the baby is not getting oxygen and nutrience as well as it could. If the placenta starts tearing off the side of the utero, then the doctors would perform an emergency C-section to make sure everything goes OK. Your wife would get a spinal instead of an epidural (just because spinal takes affect really fast). I had a spinal for my C-section.
Sleep now that you can! You will not be sleeping well for a good while. We got lucky with our girls as they started sleeping full nights at 4 months, had no colic etc, but the first while was tough. I was pumping milk every 3 hours around the clock, husband got back on the road (racing season started) when girls were 6 days old and I was alone with them 24/7.
Once the baby is here, tell your wife to EAT well, drink her water, sleep when the baby sleeps and let the house go. It doesn't need to be clean all the time. She needs to rest! If you can get the freezer full of dinners, that would make things even easier for you or order in. The less she has to worry about the daily routines the better it will be and hopefully she doesn't get PPD (post-partum depression). If you see any signs of that, contact her OB ASAP.
And most of all ASK QUESTIONS!