Is the Bible infallible?
Yikes! Tough question!
Answering this question would require a complete understanding of truth, or else you can't compare something else with it to see if there's a match. And since mankind has not reached a consensus on the definition of truth, any statement that contains references to truth is vague at best and limited for sure.
The answer depends entirely on the standard you use or the stage upon which you unfold your arguments. Take the number pi for instance. Ask any mathematician if pi is always 3.1415... and most will say yes! But a mathematician with a slightly broader scope will calmly inform you that the value of pi will continuously change if you travel along a circle on a hyperbolic surface. The value or even the constancy of pi can not be addressed if the geometry is not declared. Same with the Bible
If you want to think about things you need first state your 'operating system.' Are we using math (so that 1+1 is always 2) or poetry (so that 1+1 may be everything or nothing)? Are we using tried laws of logic (upon which everyone will agree) or are we using our own beliefs (I am right, no matter what others say)?
And if you want to ponder the infallibility of the Bible, which one will you use? There are many different translations, all marvelously inept to convey the vast intricacies of the Hebrew and Greek texts. Back to the source texts, you say? We don't have them! The Bible is a compilation of works that in turn are compilation of even older sources. We don't have the original works of Moses, or the original descriptions of the Temple, or any of the other stories. The oldest extant copy of the Hebrew Bible is about 1000 years old, and the oldest fragments are from 200 BC.
But the real question is: should we expect the infallibility of God's word to be vested in verbal details, as if it were a computer code that freezes if only one bit falls over, stern like a graven image? Or is the Bible much more like nature, where variety makes all the difference and apparent contradictions result only in greater complexity?
Here at Abarim Publications we are devoted to Bible study on all levels, and have been doing it for decades. Yet we too don't have the answers. But we generally oppose the idea that the bridge between God and humanity rests on intellectual rigidity. Any high-ranking academic may study the oldest Hebrew texts for a life time and still remain unmoved, and any kid can pick up an old dog-eared NIV and read with an open heart and become forever changed by God's Spirit.
Just like the perfection of the bride lies not in the bride but in the love of the bridegroom (Ezekiel 16:14; Song of Solomon 4:7), so lies the infallibility of the Bible not in the Bible but in the infusion with the Holy Spirit.
Bottom line: God doesn't work with golden calves, no matter how shiny. The question on the infallibility of the Bible itself is flawed.