In Barth's foray into doctrine of God he makes the modest claim that more or less every pre-Reformation and post-Reformation theologian got the doctrine of God wrong. Theologians today work in the wake of this claim. Some agree with Barth, and try to continue along the same path that he walked, though not uncritically. Others agree, but seek to find alternative solutions (some of which are more alternative than others). And others simply disagree, and seek to keep alive what is in danger of being lost.
Barth's criticism can be summed up as follows: theologians have confused theology with metaphysics. What does such confusion look like?
Barth gives one such example. Take the divisions we might make between nature and grace, body and soul, visible and invisible, material and spiritual, earth and heaven. You will finds these divisions all over so-called "classical theology". God is generally associated with the latter term, and creatures are associated with the former term. So, for example, we associate God with "spirit" and "supernatural" and "invisible" and "heaven." Barth's point is that the differentiation of the divine from the non-divine does not coincide with these other distinctions. In other words, God is as much to be distinguished from the "supernatural" as He is from the "natural", or from the "spiritual" as the "material". So if we think we are in the realm of true talk about God when we talk about spirit, we are gravely mistaken. According to Barth, it is no more anthropomorphic to talk of God's hands or feet or back than it is to talk about the being of God as spirit.
With this Barth basically dismantles the work of my former teacher, Maximus the Confessor. Maximus was of course much too sophisticated to identify God with any human word, be it spirit or being or absolute. Indeed for Maximus God so transcends Being Itself that He is perhaps even more like non-being than being when conceived by us. Nevertheless, the metaphysical hierarchy is present: spirit, intellect, soul are closer to God than matter, senses, and body.
Barth's argument is that we cannot equate God with the Invisible, or Incomprehensible, or Absolute, or Ground of Being. God is as different from the invisible as He is the visible. Or on the positive side, God is as free to be associated with the visible as He is with the invisible. We don't get closer to the "pure essence" of God when we approach God with our metaphysical i's dotted and t's crossed. There simply is no way from here to there.
The takeaway point in all of this?
People in "sophisticated" (post)modern Churches would do well not to identify God with absolute spirit or the unknown ground of being, whereas people in "unsophisticated" evangelical Churches would do well not to identify God with the supernatural.