Hand Picked Bible Applications

I understand that my question pokes at a sensitive area, but being a nonreligious person in a largely Christian region, I find it extremely dissatisfying to leave such a core aspect of my neighbor's lifestyles to mystery. My question is this: With the abundance of Biblical passages, in both the Old and New Testament, how do Christians rationalize the specific stress and emphasis on only certain sections of the Bible? The Bible contains loads of information, some of it pleasant, some of it frightening, some of it seeming to be downright silly. For instance, people often quote Leviticus on denouncing homosexuality, and yet Leviticus also writes against eating shellfish and wearing cotton/polyester blend clothing. I'm also fairly certain the Judeo-Christian stance on women and slavery has changed over the past few millennia. Beyond that, the Bible has been translated by hand between multiple languages, and been reviewed, revised, cut, and supplemented by several religious authorities. If the entire Bible is the infallible word of God, how can his followers assert their own judgement over his by themselves choosing which parts of the Bible are true or applicable? The aforementioned followers being of course, the Pope, translators (Monks, probably), Priests, but mostly everyday, normal Christians. Thanks.