Question: How do we know that dark matter is dark, in the sense that it doesn't give out any light or absorb any? It is impossible for humans to be watching every single wavelength. For example, what about wavelengths that are too big to detect on Earth?

Answer: 
If dark matter emitted very long wave lengths of electromagnetic radiation it would mean it is composed of charged particles. There is no escape from that conclusion. Somebody might propose that dark matter is some strange configuration of charged particles which acts as a very long wavelength antenna. That might be a good model, but there is a hitch with it. If it emits longer wavelength radiation it must be colder. The Wien displacement law is that $\lambda~=~c/T$, for $c$ a constant, which may be calculated, but is not relevant here. For $T~=~2.7$K the wavelength of radiation is $.1cm$. Let me assume that there does exist some very long wavelength radiation, say $100m$ as the lower bound on this. The ratio of temperatures gives that
$$
T\_{100m}~=~\frac{10^{-3}}{10^2}2.7K~=~2.7\times 10^{-5}K 
$$
So all this can be is a very cold gas, which is the hitch. This gas is much colder than the background radiation and not in equilibrium. So from some physical grounds this is not likely, and dark matter is most likely not some ordinary form of matter that interacts by EM.
Adding two points that havent' been made here yet:

* I would argue that observations of Baryon-Acoustic Oscillations in the power spectrum of the Cosmic Microwave Background are actually the strongest evidence that the universe contains a large amount of matter that clumps under gravity but does not feel any photon pressure.
* Since dark matter doesn't interact via electromagnetic radiation, its name is a misnomer. It should be called transparent matter instead.