Can you eat the placenta?

You can but ...: This is referred to as placentophagy and has been part of many different cultures in the past - and even present. But like consuming any "meat" it can transfer blood/tissue borne infections and must be prepared and stored in a fashion to prevent spoilage. I wouldn't encourage this practice, but to each his/her own.

Yes,: I've also seen them used for plant fertilizer, different cultures think differently