I'm sorry, but I fail to see how it is very testable. I very much like the main conceptual point "it is the antiferromagnetic interaction that is universal while it is the fermiology that is not". To this end, the authors pose (definitely not derive in any way) an extremely simplified model, that nevertheless is seemingly capable of accomodating the wildly varying behaviours we see in unconventional superconductors. It is consistent with many observed properties. However, perhaps due to its versatility, to me it doesn't seem to have much predictive power, and certainly not quantitatively. It may be perhaps be falsified by some new class of materials, but even that seems not very straightforward to me.

They put the paper on arXiv before publication, so I guess exclusive is not as restrictive as it may sound.

Come on people, how hard is it to include the arXiv link? Just google the title, it's usually the first hit.
http://arxiv.org/abs/1207.5832

Indeed. The fact that they didn't put it on arXiv is another indication it's probably not much more than hype.

Now that I think of it, how awesome is this? Being published in a journal but not on arXiv is more suspicious than the other way around.

DOI is only a link to the official address of a paper, it is not a repository.

Yeah, sorry, it's both hadrons and leptons.

That question is a bit difficult to answer. Let me try a few, hopefully one of them helps you.

1) It's there because it works. A large part of high-energy theory is what is called model building, where people build models that at the least agree with previous knowledge and are internally consistent. Hopefully they also explain something not explained before. Such a phi^4 potential term is very natural to try (cannot elaborate on that here), and gives the Higgs boson and mechanism as we know it, and thus the Standard Model.

2) The phi^4 is the reason for the self-interactions, agreeing with observation.

3) This one is complicated. The Higgs potential energy contains two terms, one proportional to phi^2 and one proportional to phi^4. In quantum field theory, terms quadratic in a field correspond to the mass term for that field. Without the phi^4, the Higgs would be a free, non-self interacting particle. Moreover, the whole reason why the Higgs field can give mass to other particles, is because its mass term is negative! This is called "spontaneous symmetry breaking", a hugely important concept associated with phase transitions. You can picture it as follows: a ball in a valley will roll to the bottom and stays there. The negative mass (potential) term however causes the middle of the valley to rise to a small hill (local maximum). The ball will now want to roll down away, but any direction is equally good, and one is chosen randomly or "spontaneously". The phi^4 term is necessary to make the valley curve upward again, so that the ball does not roll down indefinitely. Thus to have any model with spontaneous symmetry breaking (which agrees with the fact that the Higgs field permeates all of space), a phi^4 term is necessary to make the potential energy bounded from below.

Just want to mention that for all the "ordinary" particles, that is the hadrons, the Higgs contribution is only part of their mass. Only the mediators of the weak nuclear force, the W- and Z-gauge bosons, get all their mass from the Higgs mechanism, which is the reason why this force is short-ranged, as opposed to for instance the electromagnetic force mediated by photons, which is (infinitely) long-ranged.

English language version:
http://ajw.asahi.com/article/behind_news/social_affairs/AJ201205250024

The expression "quantum fluid" can be misleading.

What they did here is make a system of coherent "polaritons" just as laser light is a bunch of coherent photons/light waves. As mentioned in the article abstract, a polariton is some combination of a photon (light particle) and an exciton. In turn, an exciton is a bound state of an electron and a hole from the semiconductor. (A hole is the 'vacant' positive charge created when an electron is removed, and may for all practical purposes be regarded as an anti-electron within the semiconductor.) If I understand correctly, the novelty in this work is not making the polariton condensate but the visualization of it. In that sense, the summary if way off.

This is surely not easy to grasp for the layman. What does this imply? As parent mentioned, making coherent quantum states or matter is a standard affair by now, and research focuses on extending our capabilities on all levels. It is necessary for our understanding of the fundamentals of quantum mechanics and how many particles conspire to make laboratory but also everyday matter. The practical possibilities for making devices out of "quantum fluids" is severely limited, since you almost always need extremely low temperatures to produce them. Only superconductors come close.