What is the link between observation wavelength and spatial resolution of an instrument? It seems that when capturing and emitting EM waves matter proceeds differently depending on the wavelenght. According to an answer from another question, EM energy is captured following three modes: electronic transition (e.g. for visible light), rotational and vibrational absorption. To which we can at least add induction phenomena (e.g. radio wave) which works in an unrelated way.
Morover diffraction limit imposes restrictions on the finer details observable.
How the frequency and energy capture process used to observe an object affects the resolution at which we can observe the spatial features of an object?
A corollary question is: are there regions of the EM spectrum that cannot be observed because there are no possible instrument sensitive to these frequencies?
 A: The answer would have to depend on a specific scale. i dont think there is an answer to this question without determining a scale.
A scale will fix the dimensions and the relative wavelengths that are relevant to the spatial resolution of objects.
Lets say one wants to observe a cubical object which radiates (very high at ultra-violet).
At visible wavelengths the spatial features of the object are determined. At ultra-violet the spatial features (for the same scale and distance) will be blured due to the amount of radiation at that wavelength (the object will glow intensely there, thus boundaries are blurred).
Effectively a boundary is similar to a phase transition between areas of different wavelengths (thus the resolution wavelength can give different boundaries for same object).
Plus the spatial features even in visible wavelengths can be blurred due to atmospheric distortions or attenuation or shifts over distances (which are comparable to the range of wavelength used in the resolution).
A: Only the last part of this question is amenable to a straightforward answer. All wavelengths are potentially observable using different techniques, from gamma rays through to very long wavelength radio waves, over at least 13 orders of magnitude in $\lambda$.
Some of these wavelengths - Gamma rays, X-rays, UV, far infrared - require space-based observatories because the respective wavelengths do not penetrate the Earth's atmosphere - e.g. Integral, Chandra, IUE, Herschel. The rest can take place on Earth, though there are advantages in doing these from space too, either because the atmosphere blurs the image (optical - HST), or because Earth-bound interference can be a problem (radio wavelengths).
The biggest factor that affects how much detail can be resolved is the aperture of the instrument. The best angular resolution in principle is $\sim \lambda/D$. This can be approached by optical/ UV telescopes in space, but it is difficult to put big telescopes in space. On earth, the biggest 8-10 m optical/IR telescope approach this limit using adaptive optics to remove the blurring effect of the atmosphere.
At longer and shorter wavelengths there are different problems that stop this limit being completely reached. At radio wavelengths, huge diameters are needed to get even close to the angular resolutions of optical telescopes. This can only be achieved by linking radio telescopes together into arrays and using interferometry techniques - synthesising larger apertures. An excellent example is the mm-wave ALMA array that will soon be operational in Chile.
At short wavelengths, there are no effective lenses to focus the light. X-ray telescopes must use nests of grazing incidence mirrors. Whilst these achieve resolutions that can now approach those of ground-based optical telescopes (e.g. Chandra), the compromise is limited collecting area. Simple lack of photons can also affect the ability to resolve details in this part of the spectrum. At gamma wavelengths this is even more the case. Ingenious solutions include "coded masks" to perform imaging, but it is not possible to get anywhere near the fundamental resolution limit.
Your question is very (too) broad and I have limited my answer to an astronomical perspective. Apologies if this not what you were looking for.
