There are several problems to overcome for a much wider range of wavelengths (and I don't know a solution, so I'll just list these):
The sun will have to produce light in those wavelengths, otherwise you may be able to see them but it will be dark;
Ultraviolet and shorter wavelengths are ionizing, meaning they cause chemical changes (damage). Think sunburn to much more damage at shorter wavelengths. In a world that doesn't protect against this kind of light, life is unlikely to arise at all, and whatever does arise will want to protect against this, not use it to see.
Water is very absorbant in most of the infrared region, and eyes contain lots of water making them non-transparent. The sensitive parts would have to be immediately on the outside of the skin, and the atmosphere shouldn't hold much water.
At much longer wavelengths (like radio), you also need equally long antennas to detect them. Getting any kind of resolution would need eyes the size of radio telescopes (eyes would be radio telescopes).
Finally, you have to consider whether the kind of thing you want to see is actually opaque at a given wavelength.