I think the critique against Barkley is that watching him flounder around towards some sort of knowledge about the issue is inefficient. You are right to suggest that we should be open to all viewpoints, but the argument against Barkley is that he has not developed a viewpoint yet. It is like trying to learn physics by having your not-particularly-academic cousin report his understandings from his Physics 101 class every week. Your time would be far better spent speaking with the professor instead.
What’s worse is that Barkley seems to have control over the direction of the show. Lacking understanding of the issues — he seems new to the most basic aspects of Islam, for example — Barkley is unlikely to efficiently steer the show towards new understandings. As a number of people in the comments have suggested, the show might have benefited if it were directed by someone who already understands the issues.