When Commander Koenig flies out to check the problems in Disposal Area One, the activity there lights up the sky in bright flashes from beyond the horizon. However, there is no atmosphere on the Moon, and therefore nothing to be "lit up". There would be no visible effect beyond line-of-sight.
A tremendous explosion on "the dark side" of the Moon supposedly throws the Moon out of orbit and into deep space. There really isn't a "dark side" to the Moon. Though it is true that only one side of the Moon ever faces the Earth, all parts of the Moon get sunlight as it orbits Earth every month. Even if they meant the "far side" of the Moon, the situation is no better. If they actually meant "dark" side (ie: the side facing away from the Sun at that moment) then the explosion would have flung the Moon into the Sun. If they meant to say "far" side, then the explosion would have flung the Moon into the Earth.