I read him not as suggesting that the public should decide what is good science, but in suggesting that it would be beneficial for more actual science to be done on subjects that interests the public, even if more conventional journal considers it beneath them and funding agencies don't consider them important.
Such as this time travel paper: Clearly it capture public imagination, even if the result was negative.
I'm honestly not sure what outcome he's asking for, though. This paper did capture the public imagination! He put it on arXiv.org (where it was accepted after their very minimal but non-zero peer review), and within days he was doing a whole bunch of press interviews.
What was he hoping to accomplish beyond that? Is this about getting another entry on the peer-reviewed publications list in his CV? The paper probably isn't worth that, at least as work in physics. But he's welcome to add a section to his CV about "public outreach" and talk about it there: he'd probably have a lot to say.
Can you elaborate on "beneficial"? Beneficial for what? Sure, perhaps the time travel paper captured the public imagination. But so does movies and novels.
Though I didn't see him talk about it at length in the blog, I can see that he might have meant that such a journal would be good for interesting future generations in science. But is this really a good idea? They would come into physics, or whatever, with the expectation that such research actually constituted hard science. It is not.
Interesting future generations about science is hugely important, but this is just a dishonest way of doing so.
And also, this may sound a bit harsh, and I might be out of line here, but I think the point of the paper was really to get some attention. And personally I think there's a trend of this happening in physics' interface with the public -- scientists wanting attention for themselves, apparently for the sake of future interest in the field. There seem to be a lot of popular science books these days, many written by genuinely brilliant scientists, who seem to be trying to sell their own theories as truth, like the various string theories and other GUTs. While I am sure that the authors don't really mean to say that their theories have passed the sniff test of science, and that we can put their theories on the same shelf as GR and QM, my observations from friends and people on the internet tell me that a lot of them just gobble it up as truth.
PS: Not saying that the GUT formulations are in anyway comparable to Nemiroff paper.
Such as this time travel paper: Clearly it capture public imagination, even if the result was negative.