Today I tried to search in Facebook about stackexchange. I found stackexchange itself and some stack exchange sites have their individual facebook page. So I feel movies.SE should also have a facebook page and whenever a new question would be posted the question would automatically be shared on the wall of the people who would like this page. This way we can draw more attention of the users and make it more busy. New users also can connect to this site more easily and users can also share the questions directly from their facebook profile. I observed several avid users tweet frequently the questions, but sharing in facebook is very rare.
We already have a Twitter bot (that is controlled by the system and none of the moderators)
As far as a Facebook page, I'd have to talk to the higher ups about what would have to be done sbout that.
Further updates pending