[pessimizer]

Paid moderation. Putting up an open image sharing site with no security is akin to opening up a nightclub with nobody checking ids at the door and no security.

I can't tell you what to do to meet the minimum legal standard of covering your ass, but that's going to vary by jurisdiction and current whims over time. I can tell you, though, that by the time somebody has stumbled over a terrible image and reported it, they 1) will be horrified by your site and never use it again, and 2) the poster will have shared the url with everyone they wanted to and the image will already have been distributed as far as it was intended to be. If the number of terrible galleries is increasing, you're probably becoming well known within tiny circles as a convenient place to share the stuff.