Some of these are legitimate. Ultra-high energy cosmic rays do seem to exist, and it’s very difficult to explain how they’re possible. I’ve seen a variety of explanations, but none particularly satisfying. I’m not sure I’d put them in the top 13 mysteries of science, but they’re a legitimate puzzle.
The horizon problem was also a puzzle, but the inflationary theory seems to solve it adequately, along with several other puzzles of cosmology. The causes of inflation are still a problem, but that’s actually very closely related to the dark energy problem (mentioned later in the article), and not nearly as bad.
The dark energy problem, as described in that article, is if anything underhyped. As I mentioned in another current thread, naïve attempts to estimate the strength of the dark energy are off by 120 orders of magnitude, which probably represents the largest numerical error ever in the history of science.
Some of the things they mention are genuine, but overhyped. We don’t currently know what dark matter is, but there’s about ten thousand things it might be. Every time a particle physicist hypothesises the existance of some new particle, there’s always an afternote that this new particle might account for the dark matter. And at least some of the dark matter (though not all) is just perfectly ordinary familiar stuff that just happens not to be glowing.
The WOW event, and it looks like the tetraneutron, are both single, isolated events. Without some repeatability, it’s hard to make anything of either of them. And even as isolated events go, those aren’t the biggest: I’d give that honor to the apparent magnetic monopole detected at Stanford some time back. Magnetic monopoles theoretically ought to exist, but estimate of their density generally put them at about one in the entire volume of the observable Universe, so if that one just happened to pass through one of Stanford’s detectors, it’d be quite a feat. But the recorded even had exactly the right characteristics for a monopole detection, and I haven’t heard any other explanation for it.
The Pioneer anomoly and the variation of fundamental constants are both effects burried in noise. In neither case is it possible to thoroughly enough eliminate possible causes of experimental error. Both are interesting and worthy of further discovery, but the evidence is not yet extraordinary enough for the extraordinary claims being made (a point Dopers should appreciate).
And at least one of the “puzzles” they mention is bunk. Cold fusion was and is a collosal blunder at best, and an outright fraud at worst. It’s conceivable that we’ll someday figure out how to do it, but there’s no reason to expect it, and certainly no evidence that it’s been done.