No mirrors are 100% perfect either. That's often the problem I've heard of with anything like this. (See
Perfect Mirror for the theoretical, but look at the image in the
Reflectivity article for typical mirrors) Let's say a mirror is 99.9% reflective (a
Dielectric Mirror can hit this, and beyond, because it's single-wavelength), which means it's absorbing 0.1% of the energy. That means that for a megawatt (1,000,000W) laser, the surface has to absorb and tolerate 1,000W, or 1kW of energy. That's not massive, but still is non-trivial, and then requires additional cooling to the surface to KEEP it reflective (if it melts, obviously that's bad).
Any word on the numbers they're talking about for the military lasers? That'll give the numbers some realism.