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Best practices in community management, brand awareness and content marketing actually expect you to keep the bad comments on your/brand's blog.
It adds character and credibility to the blog and you as a personal brand or otherwise. A blog with negative comments is a bias blog.
Turn a single comment into a thread of constructive criticism. Any thoughts?
If I see that the negative comments can serve as vehicle for improvement, I consider them. But if they are just meant to ruin my reputation, I dump them.