[ceptimus]

I would say that, at any moment in time, half the moon (the side facing away from the sun) is dark - in just the same way that the half the earth facing away from the sun is dark - what we call night.

When the moon is new (as seen from earth) it's between the earth and the sun, so the dark side isn't so very dark as it's lit up by earthlight. When the moon is full (as seen from the earth) then the dark side is very dark - it's only lit up by the starlight and (if they're above the horizon) the outer planets.

So what we correctly call the 'far side' - the side of the moon never seen from earth - does get darker than the near side. Although it's confusing and mostly wrong, there is some slight truth in calling the far side, 'the dark side'.