The missing mass problems are several sets of observations that could be explained if there were some matter that has mass (interacts with other matter via gravity) but does not interact with light. The same distribution of this missing mass would explain all of them. All competitors that have been explored fail to explain at least one.
I only partially understood the evidence explained in the wikipedia article, but let me try to summarize the major pieces of evidence that I understood.
Historically, the first piece of evidence is the galactic rotational curves. If you have an object with a mass distribution, you can predict different parts of it should rotate about the object's center of mass. When astronomers apply this idea to galaxies, they find that the stars far away from the center move faster than they'd expect based on the mass distribution that they can see.
Gravitational lensing is a result of general relativity. When one massive object is in front of another object, the mass from the front object distorts the light that arrives from the rear object. Astronomers infer the mass of the front object by how the appearance of the rear object changes when the front object moves out of the way. General relativity is the only theory that has successfully described this phenomena, and it predicts that the mass must be there.
Finally, several experiments have measured the cosmic microwave background radiation in quite some detail. This background radiation looks almost, but not exactly, the same in all directions. This variation is called the anisotropy. I don't fully understand why, matter that interacts with light has a different signal in the anisotropy than matter that doesn't interact with light. So by measuring the anisotropy in enough detail, astronomers can infer how much normal matter there is, and how much dark matter there is.
The dark matter community talks about "candidates" for dark matter. These are particles that could be the missing mass. The Scientific American article you cite is about one experiment that is looking for a specific candidate. Supersymmetric particles are another candidate for dark matter, not a competing theory.
Both of your other links set off a lot of red flags for me. The Electric Universe really looks like it's just a crank with a pet theory. It doesn't seem like it's even trying to address the anomalies that dark matter explains; it's only trying to argue against black holes. Their theory will not explain any of the missing mass anomalies. Science 2.0 looks like it has a mix of good and bad content. The particular article you cited is about MOND, modified Newtonian dynamics. The idea is to modify either Newton's second law ($F = ma$) or Newton's law of universal gravitation (so that the force due to gravity would fall off as something other than $r^{-2}$). MOND was originally invented to explain galactic rotation curves, and it does that. Its problem is that it doesn't explain, for example, gravitational lensing.
