Thoughts?
I don't know enough about Barth to comment.
Kung and Barth are/were theistic evolutionists which carried to its logical conclusion is mankind will ultimately be like god. Kung also is in favor of euthanasia which seems to be a contradiction in evolutionary thinking.
Well, he didn't believe that the Scriptures were the word of God, he believed in Universal atonement, that the creation story was a myth, he had a Romanist view of justification, his political views devolved to Stalinism, or at least a defense of Stalin;
My guess is that he would have been a big fan of the current Pope.
For additional reading, you might try http://www.trinityfoundation.org/journal.php?id=147 There is a brief discussion on the Puritan Board that I didn't find particularly helpful but for the link to the Trinity Foundation item above.