I'm going to answer this from my experience with laser cutters.
Mirrors are used in laser cutters to transmit the laser from the source to the cutting head, so it is possible to reflect lasers.
As @ArtificialSoul mentioned, mirrors don't work with every wavelength, so you change the laser wavelength (ie: change the source radiation) and the person behind it is toast. Go from a CO2 laser to a solid state laser and you change wavelengths.
Dirty mirrors don't really works. As @PChapman suggested, mud, dirt, dust, or anything that sticks to the mirror is going to burn, which damages the mirror, decreasing it's effectiveness, causing the mirror itself to heat and then break. When this happens in a laser cutter, you get time to replace the mirror, since it stops cutting as easily. Clean the mirror, and you're back in business.
A dirty mirror could be prevented in certain instances by using hydrophobic materials, though.
Scratches and pitting in the mirror are not as bad as dirt (in some ways), but it still reduces the effectiveness of the mirror, causing heat, and eventual destruction. It also has the added detriment of being permanent.
Something that would work, to a limited extent, as a defense against lasers is a filter. Most laser cutters have a view screen to see your material being cut. This is usually a piece of glass or plastic that is treated or naturally filters out/absorbs the specific wavelength of the laser. Most of these materials absorb a large variety of wavelengths while many allow visible light through.
Acrylic is used as a view screen fairly often, because it absorbs the laser wavelengths naturally. This is the same reason it cuts so well on a laser cutter. Acrylic plastic can come in clear, without reducing it's laser absorbing capability. So, you can have a shield of acrylic, but it'll eventually be cut through, depending on the strength of the laser pointed at it.
Your soldiers can have their eyes protected from some indirect laser light by using the same type of laser goggles that people currently wear to protect themselves while laser cutting. Some of these are made with acrylic.
BTW, here's a link where you can get information about laser wavelengths and what kind of protection you need against them. It includes all kind of safety goggles, windows, and other documentation.
As an added bonus for you, polycarbonate, which also absorbs laser light effectively, is a material used as "bullet proof glass". Polycarb generally isn't used as laser cutter material due to it burning rather than vaporizing. It also comes in clear. You might be able to layer acrylic and polycarb together to get some sort of extra-strength laser and bullet proof material for shields and tank view ports.
With polycarb, the laser reaction is very visible, so you could use this as a way to locate where the laser is coming from, as most lasers are invisible to the human eye. Also, any laser strong enough to burn something from a significant distance is strong enough to make a person blind instantly. Even if the eye is left intact, the optical nerve will be destroyed. Anyone who gets a laser weapon shot across the face is simply, instantly, blind. Period.
A surgeon would have to replace the optical nerve to have even a chance of sight again. I don't know of any electronic devices available today bypass the optical nerve to restore sight to people or not, so that might be more research for you to do.
EDIT: I did some testing with the laser cutter I use, and here's the video: