A "flag content" link should be good enough. Sounds like you're US based; you're not required to manually check all user-contributed content. Set up a DMCA section and link to it at the bottom. If LEA contact you, make sure you react fast, and maybe you want to offer them an automated way of takedown if this really happens that often.

For the future: Asking legal questions without stating your jurisdiction is... not helpful. :)

Yes, big sites employ a lot of people to clean content. I remember reading an article about poor people in $third_world_country that do this all day long.