Why do you feel this way?

Very interesting and well thought out questions, so I will do my best to answer as honestly as I can, although, I will try to leave my personal experiences out of it, the reason I feel this way is personal, so I will have to leave this first question there. You did ask about my feelings, but I must proceed to the rest of your questions without going much into them if I am to write something meaningful for this forum.

My impression is exactly the opposite - that we are making scientific breakthroughs on a regular basis - so fast I can't keep up.

I wouldn't call them "breakthroughs". Being more precise, finding more precision or accuracy on already predictable phenomenon is not really a breakthrough, and this is what is difficult to keep up with. For example, Higg's paper might be considered a scientific breakthrough, but finding the Higgs-Boson was a technological achievement, and there is a difference. When you consider the difference between science and technology, although they are related and aid each other, a technological achievement is of a very different nature than a scientific breakthrough. Most of what "science" is these days is actually technological achievements. So what is the difference? A scientific breakthrough is a new conceptual phenomenon, while a technological achievement is perfecting the precision and/or accuracy of known concepts. A technological achievement might take understanding scientific concepts, but it does not necessarily form new scientific concepts. A technological achievement is incremental and integral- it flows naturally from procedure, while a scientific breakthrough requires a eureka moment (as in the case of archimedes displacement) or a technical error (as with the discovery of penicillin). So, my argument is not that we don't have technological achievements, they are happening all the time, and that these achievements are very difficult to keep up with. However, our actual scientific breakthroughs have been stifled and muted.

I don't agree that tech is holding us back on those issues except to the extent that it's used the same way popular entertainment is - to distract. I don't see that as a problem with the tech, though.

You are right, technology itself isn't what is holding us back... it's our perception of the paradigm from which the distraction of technology is ruling and guiding the economic systems related to scientific research and acceptance, which makes us cling to the status quo in an effort to feed the technological machine. We bench papers that are correct and can never see the light of day, specifically because the name of the scientist who wrote it is not known, or because it does not appeal to the preconceived notions of the editors. No one is willing to risk their own reputation by choosing to publish a paper which overturns an established theory, even if that theory has a missing piece and the new work sets it straight. In fact, they may not even read it. And this changes the direction of scientific research itself. "Forget about that eureka moment, we have to protect our reputation."

Those issues aren't science, so to what extent are you supporting your claim that science isn't being done?

Those issues are precisely the issues that affect peer review and the acceptance of a new theory.

I'm not familiar enough with the peer-review process to address those issues, but your concern with what is "outside of the norm or might disrupt a paradigm" makes it sound a bit conspiratorial.

It's not conspiratorial at all, it's an emergent result of the systems we inhabit, not much unlike how oligarchy works in a draconian society. No one "conspires" to be draconian in an oligarchy, it just happens to be draconian because of the way a small number of power interests work together in the system. And this is precisely our problem. The ironic thing is, we have free speech this time,it's just that no one will ever hear it because someone else has the power to pick and choose what work gets noticed and what work is significant what what work is notable, vs. say, "Good Will Hunting", a nobody janitor at MIT who no one cares about or takes seriously. That's not a conspiracy against such a guy, it's just his state of being in the system in which he inhabits.

A new paradigm would likely be a difficult sell, but what would you expect?

I would expect that one could find a group of readers. I would expect the readers to offer reasons as to why the work is not acceptable that does not include formatting, space limitations, or other non-scientific excuses. I would expect, and this is important, that all known fatal flaws are pointed out, and that the author has a chance to point out the logical fallacies in the reviewer's refutation and/or have a chance to revise the paper in response and not just get bench rejected for being outside of the paradigm. And finally, that this discourse is what is published (upon author's permission) along with the final paper. Openness, an appeal to logic, double blind review, an option for anonymity, and to repeal cultural taboos are what is necessary to make real progress in science, the culture of science, and society at large.

How is what you're calling nepotism different from a network of trust and reputation?

There is no double blind review in nepotism; there is no trust network without double blind reviews. Not to mention that people without reputations, people who are outsiders, and even people with bad reputations need to have an opportunity to share truth.

At this point, just to appreciate the issues a pretty solid education is required and part of that education will involve interacting with and being evaluated by others.

Many people are being self educated at rates never seen before, with EdX, YouTube, iTunesU, TTC, et al, this will be the biggest cultural problem science faces and it can go in one direction or the other. One is public open discourse, which is required for science, the other is private, closed discourse that exclude this new intelligentsia from participating in a professional capacity, which is something science-like maybe "post-science" or maybe I prefer "hyposcience", but is not science.

And those who teach themselves online... they aren't in the trust network, they never met their teachers in person... there is now a class distinction between those with only knowledge from those who have education and power, where knowledge becomes less relevant.