There are objective ways of finding out some classes of mistakes. Fallacies are well-defined and most of them can be easily diagnosed. I often do this at Facebook to blow off steam.

Even better: the website can accomodate for this. It's as easy as adding a "report logical fallacy" button next to each comment. Moderators can award points to all who noticed the correct fallacy. A leaderboard can be put up. It can be made a sport.

Another benefit is that those who make mistakes receive detailed feedback.

Edit: I'd like to learn why this was downvoted. How might I be wrong?