Can a brown eyed father and a blue eyed mother still have a blue eyed baby?

Sometimes. Brown is the dominant gene, but if I remember from my high school science class, you can have a recessive gene for blue eyes, so the chance of having a blue eye baby if the mother is fully recessive for blue but the dad is partially recessive for blue, is actually 50%... However, if the father has both dominant gene for brown, then no.