Do mirrors reflect all wavelengths of the electromagnetic spectrum? Do mirrors reflect all wavelengths of the electromagnetic spectrum?
Supposing we are using the best mirrors.
 A: Take a look at a common website for any optics manufacturer and you'll see some informative plots. For instance, let us take a look at ThorLabs, one of the leading suppliers of high-grade optical equipment. Select any mirror from their catalog and you'll see a graph that looks something like this:

(Image courtesy of ThorLabs)
This graph tells you the wavelength response of a given mirror. This is for one of their high-grade gold-coated mirrors. You'll notice it does fairly well across the provided range. This mirror, as stated elsewhere in it's specs, falls off in performance below 800nm. It is still reflective in the visible range, but mostly only at longer wavelengths (thus the reddish-yellow colour of gold). Similarly, if you look at metals like silver, you'll find great reflectivity across the visible spectrum and decent reflectivity across the IR range, but at high frequency ranges, the reflectance usually drops off. Additionally, you'll often find that coatings, whether metallic or dielectric, will drop in reflectivity at some upper wavelength. As you can see in the following graph for a broadband dielectric mirror (also from ThorLabs).

This series of mirrors were produced to have a non-conductive reflecting surface and be viable over a wide range of wavelengths. You'll notice that each type of coating still drops off, however. "But, Jim" you say, "it only shows that it falls off to 92% reflectance. That's still pretty shiny". Yes, but they only cut it off like that to highlight the response in the effective region. They provide further data in the specs that show it drops to less than 20% reflective (which is pretty low) just outside the regions shown here.
What's the point of me showing you all this? Simple, no substance we know of offers high specular reflectance across all wavelengths. This is why we have so many different types of mirrors available. You need to buy the type of mirror that is most suitable for the wavelength range you want to use. For very long wavelengths, in fact, you often find the best mirrors don't even look like mirrors in the visible spectrum.
A: I believe gamma rays do not properly reflect because they lose their energy to Compton scattering.
