Pros and cons on commenting on public review papers
I would try to answer this from the standpoint of a cost-benefit analysis.

A private conversation with the author will benefit you in that you now know the answer, and can harm you in that if your question is completely boneheaded the author will think you're an idiot.

A public conversation has the added benefit that you and other people both benefit. This is somewhat of a questionable added benefit, as oftentimes the question being asked isn't relevant to most people, but still, added discourse is often a good thing. Public discussion also has the added cost that more people can see your boneheadedness. While typically this wouldn't be a problem, as most people wouldn't ever encounter the discussion, anything on the internet can go viral, even if only within a smaller community (such as your research field). Personally, that cost strongly outweights the potential benefit. I would definitely stick with personal correspondence.