The amount of light that the moon scatters depends on the wavelength of the light. Blue light is scattered more than red light, which is why the moon appears to be slightly blue. This effect is most noticeable when the moon is near the horizon.
The scattering of light by dust on the moon is also responsible for the phenomenon of lunar eclipses. During a lunar eclipse, the Earth passes between the sun and the moon. This blocks the direct sunlight from reaching the moon, and the moon only receives light that has been scattered by the Earth's atmosphere. The Earth's atmosphere scatters blue light more than red light, so the moon appears to be red during a lunar eclipse.