Factual errors exist in the Bible, whether it has to do with two different ages of some Jewish king, or the number of children of some Jewish woman, or with the confusion having to deal with what species of living things does a bat or a hare belong to (unless they evolved into present day species), etc.
So, now it is necessary to redefine what is meant by "error." The Bible cannot err in its message of God, because it is a message of love. That much we know. If you can find anything but love in everything the Bible proclaims, you are not reading it correctly because it would be contrary to God being Love.
I will be the first to admit that I often scratch my head and say "where is love in all this?" But that is my failing and when I ask others to show me they can't either, although they claim they see nothing but love in all of it! Which is soooo not convincing indeed...
I will also be frank with you all: my faith comes from God and not from the Bible. The Bible reveals God's Creation and God's Divine Economy, but does not "put" God into your heart. I also know that God's perfect love that I know through Him is expressed in imperfect language and intellect of man.
When you mix Perfect with imperfect you corrupt the Perfect even if you don't desire it, and even if your hand is guided by the Holy Spirit simply because there are no words to express the Perfect, nor could our minds comprehend the Perfect, so our knowledge and expression of the Perfect is always imperfect.
Which is precisely the reason the Fathers held from the beginning that understanding Scripture is a special gift from God and not something to be attained by pure intellect, and henceforth not available to everyone.
Hence, the power of the simple formula we all understand in our hearts but cannot show empirically in its totality -- God is Love. Oh, we can show hormonal and electrical changes in our bodies when we feel loved, but they all fall short of what the experience of love is. Such "empirical evidence" is not even recognizable as love.
But, love, although manifested physically (poorly nonetheless) is not physical or subject to physical laws at all! It is eternal and unlimited. Those whom you love truly today you will love the same tomorrow and forever, not matter where they are, no matter how far. It transcends time and space and all physical barriers and limitations of nature.
Thus we speak of love being limitless, priceless, "great" and "warm", "burning," something we would give up our own life for, our a kidney or an eye if need be, and yet no one can put a dimension or shape to it (heart is merely an "icon" of love).
Yet, although no one has ever seen love, we all claim to know love, even how to recognize love. Love supersedes our reason and logic and we "fall in(to) love," cleaving to the one we are in love with but cannot explain why, and even admit to being blinded by it.
All these terms we use in our daily experience that is known to us as true and very real, yet they cannot be measured, described, or illustrated in their , apply, forst and foremost to God; yeah, especially to God! So, when we find Love in the Bible, we know that it is true, because we know it already. That is our infallible "proof" that the Bible is inerrant.
Now, considering your silly comment about the Mystery of the Virgin Birth, as is the case with the mystery of the Holy Trinity, etc. as jo kus says, science has no power to (dis)prove it! Nor is it the purpose of science to do so. Not is it in the power of the science to prove or disprove God. Quite to the contrary, science only reveals the unimaginable power and glory of God.
Just the fact that we learn more and more about Nature proves that with God everything is possible. We certainly include the Virgin Birth in that, and a Big Flood. But, I can see the Virgin Birth happening much more than God changing His mind as if surprised and disappointed with mankind and deciding to drown the whole rotten lot along with its animals (what have the animals done to deserve that?).
The Virgin Birth makes sense in our Salvation; drowning the whole world because we turned out wicked on God's watch is not as clear. Surely, God had other options at hand! If God's revelation to man has to do with our redemption, out of love, and return to Him, then the Virgin Birth is certainly a big part in our soteriology, and more importantly a necessary step in its realization. The Big Flood is not. God could have killed every living thing, including Noah, and re-created man just as easily.
Mat 8:28 When He came to the other side into the country of the Gadarenes, two men who were demon-possessed met Him as they were coming out of the tombs. They were so extremely violent that no one could pass by that way.
Mar 5:2-3 When He got out of the boat, immediately a man from the tombs with an unclean spirit met Him, and he had his dwelling among the tombs. And no one was able to bind him anymore, even with a chain;
This story both in Matthew and Mark (Luke follows Mark's account) are about the same incident. Matthew states there are two people while Mark and Luke state there are one. It may seem like an error until one understands that it was Jewish custom in their writings (which Matthew follows in his narration) to only refer to the person speaking. Thus Matthew is simply following the Jewish custom of only referring to one verse Mark and Luke who more fully recount the story.
I bring this up simply because people often state there are errors when, in fact, they do not understand the context or customs of the writer. This btw happens a number of places with genealogy's, etc. As far as the species of a bat or hare I would have to see what verse you're referring to.
The scriptures are very clear, if there is ANYTHING that God cherishes more it is His word. He states time and time again; study the word to show yourself approved, hide the word in your heart so that we may not sin, listen to the word to get wisdom, cast the word and it won't come back void, and on and on and on. Psalms 119, the longest one right in the middle of scripture is devoted solely to the word of God. Our Lord Jesus is the living "Word" of God. Yet reading God's word is the very thing we resist. Now if God places such high stores on His word shouldn't we?