Evidence for God from Science

I just want to start off by saying that I'm definitely not a liberal when it comes to the inspiration of the Bible. I believe it's inspired and infallible and the authoritative Word of God.

Recently, when studying Bible "contradictions," I stumbled across one about how Paul's statements of "this is not from the Lord, but from me" contradicted 2 Timothy 3:16 about Scripture being inspired by the Holy Spirit. It got me thinking about what "inspiration" actually means when it comes to the Bible. Does it really mean that every word in the Bible is meant to be interpreted as something God spoke Himself? For instance, in one of Paul's letters, he asked at the end for somebody to bring him a coat he left. It's in Scripture, so that verse is there for a reason. But is it necessarily from God?

I guess what I'm wondering is, did God speak every word in the Bible, or did he approve every word in the Bible? Obviously things like prophecy are direct inspiration, but what about the more subtle things, like the personal, cultural parts of Paul's letters, or David's recording his own personal emotions? We can learn from these things, but I wonder if they truly meet the definition of "God-breathed."

Any thoughts?

I would say approved-of only, and I really couldn't see it any other way. I'll give my subjective argument for it and then my scriptural one.

Subjectively, I feel as though God would've been more specific about certain things had He "breathed" the scriptures himself. This supposes, however, that God doesn't want Christianity to be able to support different views. The arguments for predestination can be supported scripturally; the arguments against it, likewise. And if you ever want to start a never-ending thread, invite a group of faith-alone believers and a group of works-based believers to debate their positions. Same for trinitarian/anti-trinitarian, liberals/fundamentalists, YEC/OEC, Mormons/non-Mormons, etc etc.

Scripturally, my argument is very simple:
Did Jesus feed the 5,000 (Luke 9:10), or the 4,000 (Mark 8, Matthew 15:29)? note: numbers derived from section titles found in my NIV bible.

If God spoke the words from the Bible himself, then He was off by a thousand. There are other examples of this, and I recall reading a scholarly document claiming that Mark and Matthew agree with each other in details such as the one I just mentioned (while disagreeing with Luke), and Luke and Matthew (I think) agree in order while Mark doesn't.
I believe I'm off on which book relates to which book, but the basic argument is still intact: the gospels disagree every here and there on minor details.
The message is definitely not affected by it, however, and so I hold the belief that God only approves of the scriptures.

Furthermore, the apologetics I've seen on how Noah's flood isn't a plagiarism of the Epic of Gilgamesh fall into the category of wishful thinking, in my opinion. After studying how well the Book of Mormon plagiarizes from the Bible, I just can't accept how only very minor, easily-editable details that can be changed through verbal transmission are preventing an otherwise obvious conclusion that perhaps the inspiration for the story was from their own thoughts about God.