A major benefit of working in public is that it invites immediate feedback (hopefully positive, constructive criticism) from anyone who might be reading it including pre-built audiences, whether this is through social media or in a classroom setting utilizing discussion or social annotation methods.

This feedback along the way may help to further find flaws in arguments, additional examples of patterns, or links to ideas one may not have considered by themselves.

Sadly, depending on your reader's context and understanding of your work, there are the attendant dangers of context collapse which may provide or elicit the wrong sorts of feedback, not to mention general abuse.

If you made embed-able forums for web pages and sites, you could inadvertently boost signups, and boost plugin downloads. It'd be awesome to have a third party host for user profiles linkable to my site and forum. Even if you linked facebook or something, for fast signup, server data, etc...