IINAL. This is a dangerous gray area. Read for example the NinjaVideo case: http://en.wikipedia.org/wiki/NinjaVideo . (For example, see https://news.ycombinator.com/item?id=3464060 (154 points, 875 days ago, 157 comments), in particular the second comment by murz)
It’s very different if you comply with all the DMCA provisions http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Ac... and can honestly say:
“Oh my God! I did’t see that! It’s all user generated content! I’ll delete that now!” (and you delete the copyright infringe content now.)
than
“I just finishes the selection and the official movie of the week winner is $title linked by $user.”
(Perhaps this is not the ideal solution and perhaps this is not the right thing, but if you don’t follow the DMCA to you need good lawyers.)