Well one idea is write something on your blog and link it to MIRI; PageRank will do the rest :)
Another idea - organize a public movie event with a panel afterwards. Should attract a significant sci-fi fan interest and maybe get some coverage (maybe even use it as a fundraiser?). Louie Helm did this for "Our Final Invention". Will ping him.
The panel idea - especially if this can be done early, has a lot of value, could boost discussion and also provide a possible influx here.
There's a big Hollywood movie coming out with an apocalyptic Singularity-like story, called Transcendence. (IMDB, Wiki, official site) With an A-list cast and big budget, I contend this movie is the front-runner to be 2014's most significant influence on discussions of superintelligence outside specialist circles. Anyone hoping to influence those discussions should start preparing some talking points.
I don't see anybody here agree with me on this. The movie has been briefly discussed on LW when it was first announced in March 2013, but since then, only the trailer (out since December) has been mentioned. MIRI hasn't published a word about it. This amazes me. We have three months till millions of people who never considered superintelligence are going to start thinking about it - is nobody bothering to craft a response to the movie yet? Shouldn't there be something that lazy journalists, given the job to write about this movie, can find?
Because if there isn't, they'll dismiss the danger of AI like Erik Sofge already did in an early piece about the movie for Popular Science, and nudge their readers to do so too. And that'd be a shame, wouldn't it?