Yes, even in the Salganik studies or in the real world, you have to be "good enough" in order to get a "big break", but my concern is that with the chaotic luck-dominated process that we have now, the number of qualified people (or songs, or ideas) is vastly greater than the number that do get the "big break", and their potential is being wasted. (In the NFL, by contrast, even the losing teams get paid well and provide entertainment value to fans, unlike musicians who are not lucky enough to get discovered.)
I don't see how your solution changes that, though. Assuming it's implemented properly, wouldn't the ideas that already get their big break still make it through the screening alongside others that wouldn't have, and then be subject to the whims of the people? It seems like all you'd be doing is having a layer of bureaucracy to do what the Salganik effect already does. So as an example, in the current, free-range internet, there'd be a million potential memes, of which 20,000 qualify as "good enough" for the Salganik effect, and then two or three get their big break. In your proposed system, the jury would examine the million possible memes, whittle them down to probably around 20,000, then release them to the greater public, and then two or three would get the big break from there. Extra effort for similar results.
You also have to account for the fact that people do not like being told what to believe in. You suggest sites like Reddit start doing this - wouldn't Redditors cry censorship, and simply move to a site that didn't? A jury system works in real-life courts because it's difficult to move to a different country when a jury hands down a verdict you don't like (think of the outrage after the Casey Anthony acquittal, for instance). All it would take would be one high-profile "hey look how great my idea was, and the jury voted it down!" for people to start switching over to a Reddit-Sans-Jury, and we'd be back where we started.
So you have a system that's ineffective on both sides. If it skews too lenient, then it would simply slice out the fraction of bad memes that would already be ignored. If it skews too draconian, then people will simply go to a different website.
Yes, random chance is a factor in which grassroots campaigns take hold. Luck is a factor in everything. Luck is a factor in Mr. Haselton's proposed solution as well (basically extending the "internet jury duty" idea he's pushed in many other posts) - if this campaign had been reviewed by 20 random internet-users who just so happen to be militant anti-feminists, then it would've been killed on the spot.
The luck factor of a success can be minimized by actually being better than the alternatives. In the Salganik study, though the popular songs were chosen randomly, they were chosen randomly from the better subset of songs. No "world" chose a crappy song to be popular. And that study was on a very subjective medium - how good or bad a song was. In something that is generally more agreed-upon, such as "rape is bad", the luck factor is understandably much diminished.
So just because a success has a luck factor involved, that's not a reason to cast doubt on the veracity of the success. If you run a simulated NFL season a million times, certainly the same team will not win the Super Bowl all million times. When an actual team then does win the Super Bowl, does that take away from their victory, that part of it came from luck? No.
There don't seem to be many people asking questions, so I'll bite.
What exactly is Personal Audio? Your website is slashdotted, so I can't find what you make or what your business model is. But you claim not to be a patent troll. You're even willing to come to a hive of kneejerking anti-patent-trolls and answer our questions to try and convince us of this. So, if you're not one, why not? What do you make? What do you sell? What do you do?