Wood logs can be very smoky, especially if not entirely dry, raw bituminous coal is very dirty indeed and many ‘smokeless’ fuels produce plenty enough smoke to severely stain stove windows.
When using smoky fuels always have the stove’s ‘over-fire’ or ‘airwash’ control (usually a slider above the fire-door) at least slightly open to pull extra air in above the fire, pushing dirty gases away from the window and helping them to ignite. If the appliance does not have such a control you can achieve the same effect by not quite shutting the fuelling door for no more than two or three minutes when you first light, or refuel, the stove.
Window stains can be removed by either operating the stove at a high rate for a few minutes to burn the dirt off, or using an ordinary supermarket spray bleach cleaner when the fire is cold.
The ceramic ‘glass’ commonly used for stove windows will develop very tiny cracks on its surface after a period of use, this is normal