Ok, this question is more theology and philosophy than history, but there are some historical matters, and some critical thinking, so I'll address that as much as I can and nod towards the theological and philosophical. For the record, I'm an atheist with an evangelical background.

The claim is the Bible is "the word of God, who cannot lie" and "authored by God" - I think that's the exact quote. I listened to it three times, and the phrasing is important, so if I mistook something please correct me. To support this claim the video suggests three tests. It should be true in that what it says about the universe is verified by science, it should be true in that its prophecies are correct (and mentions specifically Isaiah and Jeremiah), and that it should be available to humans everywhere.

No credible biblical scholar argues that the Bible was authored by God. It doesn't claim to be. It is a collection of different books of different genres written by different men (sometimes explicitly named in the text, sometimes named in tradition) compiled over a period of time by men. The video is slippery about what exactly they're claiming they want to demonstrate: they say at the beginning it's the word of God authored by God, but at the end they advertize their next video with the question "who authored the Bible?" They know authorship of the Bible is a fraught issue and they're setting you up for the "correct" understanding of a complicated process. Incidentally, you might check out our FAQ on the composition of the Bible, particularly /u/zosim 's description of the compolation of the New Testament.

But let us entertain the argument as it's made for a moment. For the evidence the video offers I want first to dismiss that last criterion. The claim that if the Bible is the word of God it should be widely available is totally philosophical/theological. That it is widely available (measured by translations as the video appears to do) is true NOW - Wikipedia lists it as the most translated book in the world - but close on that list is The UN Declaration of Human Rights and The Little Prince, and no one would suggest those works would become closer to the word of God for surpassing the Bible in number of languages translated.

Likewise, the claims that if the Bible is the word of God or authored by God its "scientific" claims and claims about the future should be true are philosophical. Thinking that God would give us good information about science and the future depends on thinking things about the nature of God.

The historical claim rolled out as evidence that the Bible gives us good scientific information is the claim that Moses wrote that the Earth hangs in nothing. The video says Moses wrote this c. 1473 BCE, but ascribes it to Job 26:7. Here's the King James:

He stretcheth out the north over the empty place, and hangeth the earth upon nothing.

Let's just suppose that's a statement of scientific fact and not some poetic silliness for a moment. The video is immediately in trouble with its dates. The composition of Job is considerably later than the supposed life of Moses and the dramatic setting of Job. My NIV - just a regular one from a bookstore - dates the composition of Job any time "from the reign of Solomon to the exile" - sometime between say 1000 and 600. Considerably later than the 1473 date. The other piece of evidence is from Isaiah saying the Earth is a "circle or sphere":

It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in:

The date the video gives for Isaiah is 732. That's true to an extent, but it is often thought that the later parts of Isaiah (from which this quote, and the Cyrus prophecy I mention in a second, are taken) are from a second author who wrote after Cyrus allowed the Jews to return from exile c. 550. Or about the time the video gives for Pythagoras' supposition that the Earth is a sphere.

The dates the video give for Isaiah and Jeremiah are 732 and 614 respectively. The "prophecy" that mentions Cyrus in Isaiah is in the later part of the book, (sometimes called "Second Isaiah") gives a good account of Cyrus' capture of Babylon and the return of the Jews from exile because it's telling in the form of prophecy things that already happened at the time of composition. There's a similar thing going on in Jeremiah.

So, by jumbling the accepted dates for not just whole books as with Job, but for individual portions of different books as with Isaiah, the video departs from widespread scholarly understanding of the composition and interpretation of the Bible as a whole and as individual books.

In short: Should the Word of God give good scientific and prophetic information and be widely available? Maybe? I don't know. I don't think that has to be true. The scientific claims this video mentions, if they are scientific claims, are not shocking for the time they were written. The prophetic claims appear prophetic because they were added after the fact.

I find it very amusing that the video uses secular nomenclature such as B.C.E. (before current era) and C.E. (current era) instead of the more common religious nomenclature like B.C. (Before Christ) and A.D. (anno domini- in the year of our lord)