"liberal" is a pretty precise, historical term and it really doesn't fit Barth. Ken has given an excellent run-down on him above so I don't have much to add except to underline the point about him being pretty confusing to modern evangelicals.
Frankly, IMO, unless you're embarking upon a seminary program and need a grounding in the historical roots of theological post-modernism, or are planning to interact with the smallest segment of American Protestantism (the neo-orthodox), there's really no reason to read him. His great legacy seems to be the idea that the Bible is true because of the belief of people in it. This idea has done a lot of damage to the church, IMO, and so, it may be that he is actually more insidious than an outright "liberal" since, again, as Ken has pointed out, he sometimes seems so right.
His epistemology is jacked.