My first time mother had a litter of 6 puppies on early Monday morning. Labor went fine and all 6 puppies were born within 4 hours. Mama was attentive and rested while pups nursed. About 18 hours after the last pup was delivered, she had quite a bit of thick green/black discharge that was quite foul smelling. We did count placentas with each pup and although the mother did eat them quickly, we are fairly sure there was one for each pup. We cleaned her up and took her in to our vet when they opened. Our vet thought that there was an infection at a placental site and prescribed 400mg of Amoxicillin. About 7 hours after her first dose of medicine, she had green/red/brown discharge (not thick or as much as the first time, and just slightly less smelly). Should there be cause for alarm for her second spell of discharge? Or could this be her body simply clearing out the waste from her uterus?
Througout all of this, she has been eating and drinking a lot of water. She doesn't wag her tail while in the whelping box, but will happily wag her tail as she prances out to go potty.

Did your vet give a shot to clear out retained birthing material, or even a dead puppy?   This should have been done.   However, there will be a discharge for some time post whelping.   Can you take your bitch's temperature?

It is very normal for there to be a LOT of discharge for WEEKS after whelping.  It can be green, black, clotted, and come out either in the whelping box or just when they pee outside (if you're lucky).  It shouldn't smell THAT foul, but it is largely blood and waste stuff from pregnancy - so it's not going to be totally odourless.  If it smells more foul than that, it is possible it's something other than the usual discharge.

Please make sure you see a vet who is experienced with repro issues - for example, a vet who knows that it is perfectly normal for there to be copious amounts of gunk coming out for weeks after birth - or you end up with a bitch on various unnecessary medications and treatments, many of which affect the puppies, and all of which will affect her stress levels with visits to the vets and separation from pups at this time.