the moons centre of gravity is not in the centre of the moon. It is slightly shifted towards us due to tidal forces caused by the huge gravitational attraction of the earth. stab a pencil through a disc half a radius from the centre and spin it vertically. You wouldnt expect a random point of rest would you. You would expect the most mass to be towards the earth. Same with the moon
The moon does rotate but at the same mrate as the earth, consequently the same part is allways exposed to the earth's surface. The dark side of the moon is largely un-mapped as it can never be observed from the earth
No Noodlehead, the moon is tidally locked as described by Boobesque, that means it turns on it's axis once per orbit. It does not rotate at the same rate as the Earth. Note also that the dark side is not the same as the far side. The far side is the side that we do not see, the Dark side is the side that at any one time is not illuminated, ie the dark side constantly shifts.