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.
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> **Note:** this answer is similar to [this one](https://physics.stackexchange.com/a/594505/251244) also written by me. [That question](https://physics.stackexchange.com/q/420288/251244) is very closely related and an interesting read.
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> How do we know that dark matter is dark, in the sense that it doesn't give out any light or absorb any?
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To answer your question, you need to understand how dark matter was hypothesised, so here is a summary:

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> Using supercomputers, physicists were simulating the Big Bang and the formation of the Universe, applying Einstein's theories of special and general Relativity and Quantum Mechanics, experimenting with different variables to try to arrive at a system similar to our world as it is currently.
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> As they experimented, they found that in the simulations generated by the supercomputers, the matter formed attracted each other *too weakly*; matter and gas were flung out too far during the Big Bang and could not "clump" together to form stars or planets.
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> They tried adding some "dark matter"; matter which did not interact with the strong nuclear, weak nuclear, and electromagnetic force, i.e. it only interacted with ordinary matter gravitationally. This "placeholder mass" solved the problem, and the digital model successfully evolved to the system of the cosmos we observer today.
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> The intriguing thing was that ~$85$% (!) of the universe had to be made up of this hypothesised "dark matter" so that it formed correctly.
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**Conclusion:** the universe can't have existed without this mass made up of WIMPs (Weakly Interacting Massive Particles). So let's go look for it!

*Dark* matter is called *dark* because it is *hard to detect*, even though it is greatly abundant. It is hard to detect because it does not interact Nuclear-ly or electromagnetically, and photons (light particles) are electromagnetic particles. Physicist don't assume that it is weakly interacting, it was named "dark" because it is so.