Most common obstetrics nerve palsy?
Ref. DC Dutta's Textbook of Obstetrics. Pg 511
The commonest form of obstetric palsy encountered in puerperal period is foot drop. It is usually unilateral and appears shortly after delivery or during first day postpartum or so. It is thought to be  due to stretching of the lumbosacral trunk by the prolapsed intervertebral disc between L5 and S1.
Foot drop
Facial nerve
Median nerve
Radial nerve