Whether or not you find his position plausible, the argument seems unusually defensive. And I think he's aware of the wobbliness... An oddly atypical bit of Barth.
CD I/2, p.529-530:
...every time we turn the Word of God into an infallible biblical word of man or the biblical word of man into an infallible Word of God we resist that which we ought never to resist, i.e., the truth of the miracle that here fallible men speak the Word of God in fallible human words - and we therefore resist the sovereignty of grace, in which God Himself became man in Christ, to glorify Himself in his humanity. If we cannot make up our minds for this hard thinking, let us see to it that we are not shutting ourselves off from the real word of comfort spoken to us by the existence of the Bible as such. And if we want to assert a supposedly stricter concept of the value and authority of the Bible, let us see to it that we are not moving away from the strictness of its true value and authority. If the prophets and apostles are not real and therefore fallible men, even in their office, even when they speak and write of God's revelation, then it is not a miracle that they speak the Word of God... To the bold postulate, that if their word is to be the Word of God they must be inerrant in every word, we oppose the even bolder assertion, that according to the scriptural witness about man, which applies to them too, they can be at fault in any word, and have been at fault in every word, and yet according to the same scriptural witness, being justified and sanctified by grace alone, they have still spoken the Word of God in their fallible and erring human word. It is the fact that in the Bible we can take part in this real miracle, the miracle of the grace of God to sinners, and not the idle miracle of human words which were not really human words at all, which is the foundation of the dignity and authority of the Bible.
And then, p.531:
We are absolved from differentiating the Word of God in the Bible from other contents, infallible portions and expressions from the erroneous ones, the infallible from the fallible, and from imagining that by means of such discoveries we can create for ourselves encounters with the genuine Word of God in the Bible. If God was not ashamed of the fallibility of all the human words of the Bible, of their historical and scientific inaccuracies, their theological contradictions, the uncertainty of their tradition, and above all, their Judaism, but adopted and made use of these expressions in all their fallibility, we do not need to be ashamed when He wills to renew it to us in all its fallibility as witness, and it is mere self-will and disobedience to try to find some infallible elements in the Bible.