Going through Meta, I saw the promotional grant for the Star Wars blu-rays from last September. As Brent noted here, Star Wars is one of the most popular topics here and the potential for promotion is huge.
To me this indicates that we should try a bigger contest. Gaming has had several promotions lately that have been massively successful (from my perspective, I don't know SE's) and I think something in the same vein would work here.
Wars vs Trek, a la Skyrim vs MW3. They have almost the same number of questions in the primary tags and it's a classic (if somewhat unintuitive) matchup. DVDs/Blu-rays are certainly potential prizes, I'm not very familiar with Star Trek though so I can't say what else would be.
Star Wars Week. It's been mentioned before that an annual contest coinciding with May the 4th would be awesome, but that's obviously something to consider after trying it the first time :P. Personally, I wouldn't require May the 4th specifically, but others might feel strongly about it and it might be helpful due to the minor surge in Star Wars awareness that occurs.
In any case, Star Wars has tons of content all by itself and I think focusing on it specifically could be even bigger than trying to draw in two groups of fans as above. Potential prizes are the movies, games, books, action figures ... endless possibilities.
As an aside, I couldn't help but notice that the badge icons look like the emblem of the Rebel Alliance. If a contest did happen, tweaking the icons would be the best thing ever.
It might also be possible to get Lucasfilm to support something. I don't know how unlikely that would be, probably fairly, but certainly worth trying since we could reach way more people.
Obviously SE needs to be on board here and would determine the specific format, runtime, prizes, and so on. I hope there are some good ideas here though, I'd really like this to happen! I have at least a hundred Star Wars questions to ask (seriously, don't even try me) and no incentive to make the time to do so.... :P
Does anyone else have any other ideas or thoughts on this?