Is Baptism for the Dead "Biblical" and Do Latter-day Saints Correctly Practice It?

In this Religion Today episode, Martin Tanner explains why Baptism for the Dead (not of the dead) was taught by the Apostle Paul and practiced by Early Christians. He explains how its accurate practice by Latter-day Saints solves an enormous dilemma of Christianity: How could God be just if the vast majority of people who have ever lived are somehow doomed to Hell only because they never heard of Jesus?