From an SEO perspective and from a webmaster's perspective I would love to have comments on my website and blog. I would enjoy seeing the search engines get all of that content and I would enjoy the community of friends that would develop around the topics that I publish.
However, I don't have comments turned on for the following reasons:
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Comment spammers would stink up my site with linkdrops, product mentions, beggings and trollings. I know that there is software to guard aginst these but some will still get through and it will make your site a target for the underworld of the web. The more successful your blog becomes the bigger this problem gets and it can easily get to a point where you can't scale it with enjoyment or profit.
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A blog or a website on almost any topic will require a certain amount of moderation as there will be a small number of errors, petty disagreement, and other problems that require attention. Again the busier your blog the greater these minor problems become. Volunteer moderators could help a lot with these problems.
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Saved for last is the one that in my opinion can be the greatest problem - people who have a personal jihad against the topic or the industry that you cover. If you blog is about kittens this will probably not be too big of a problem, however, if it is about one of the more controversial political, social, environmental or religious issues your blog, email, telephone and more could be placed under heavy attack. If you like this type of challenge it could be a great way to get links and traffic - it might scale profitably. But if you don't care for this type of engagement you better turn the comments - you will still get some of this but it will be at a much lower level.