I should be clear that this case hasn’t concluded yet. It seems from the way the DMCA regulations are written, that you have safe harbour from prosecution if anyone unlawfully publishes copyrighted content on your site without your knowledge. At least until you take control of those posts in any meaningful way.
Live Journal has a system of volunteer moderators who were also instructed to try and catch breaches of copyright. This system doesn’t appear to be robust or iron clad, just a filter to try and weed out some of the breaches, along with other content not useful to the site. However, it seems that by the moderators green lighting posts as not contravening the rules of the website, it could bind Live Journal as authorizing the breaches of copyright, and remove their safe harbour. The reason potentially being: The posts may no longer be considered as being made ‘at the direction of the user’, but at the direction of Live Journal or its agents.
In essence, there could be a precedent set here that a hands off approach to controlling breeches of copyright might be the safest way to deal with this in similar situations to that of Live Journal. It seems that you either don’t try and mitigate violations of copyright, or try and prevent it to the highest of standards. No middle ground. Even trying to do the right thing and filter out some breaches of copyright may be bad news for a site owner, but it remains to be seen what the final verdict will be.