The Bible contains everything necessary for salvation and is authoritative in matters of doctrine and faith.
Original Sin is a doctrine; an extremely important one. It was caused by the Fall of Adam and Eve. Thus, it is by one man that we all have broken souls (though we are not guilty of it; they were, we weren't).
As I said in a previous thread to you, you should research the Christian faith before you pick up the Bible. Anyone can pick it up and say "X is true because Y says so" or "A cannot be true because how do we know B even existed?" With a understanding of important theology, one can then apply that when reading the Bible and understand it better.
In this case, St. Paul is not mistaken. And I should note that, while Jews do not hold to the idea of Original Sin, they do believe that the Fall did occur, just differently; they believe that upon eating of the Tree, they were given the ability to choose and make decisions, thus the Jewish belief of the yetzer, or conscience. The problem is, while we may have now the capability to make decisions based on our conscience, our relationship with God has been disturbed. Our souls were broken by this one act of Adam and Eve rejecting God's direction.