Turned out I didn't like it much.
But one of the things that struck me, and pleased me, was Barth's matter of fact insistence on the reality of angels (and, in a sense, demons) and their work in the created world. He notes that angels often accompany and witness to God's revelation - the absence of angels during most of the incarnation being an obvious and important counter-point, showing that something unique is happening here, where God reveals himself and witnesses to himself, making the angelic witness doubly superfluous. But, as Barth points out, in some senses the angelic witness is always utterly superfluous. When we read in the Bible that an angel did something, we surely must understand the Scripture as saying that God did something through an angel - and if this is correct, is it not the case that God could have worked without an angel to the same effect?
So, why angels? Barth argues that their presence reminds us that God is not imminently within us, or easily within our grasp, but actually transcends our being and our understanding. Angels, coming from heaven, remind us that God always comes to us from elsewhere. Angels, turning up out of the blue, remind us that God does not come at our will but at his. Perhaps most importantly, angels keep us from an almost deist conception of God that binds him to the normal course of events, preventing him from surprising us with his presence and his grace.
I read somewhere that Francis Schaeffer used to open university missions by talking about angels. I don't know if that's true. If it is, I imagine his aim was to show what a very different, and in many ways very surprising, world we live in if Christianity is true.
I certainly wouldn't want to be without the ministry of angels.