I remember reading somewhere that technically, the moon does not revolve around the earth, but the earth and moon revolve together around a common point. this point is close to but not exactly the rotational axis of the earth. The result of this is that the earth tends to move side to side in its orbit.
Is this true? Just curious, and wide awake at 5:20 a.m.
Correct. Here is a diagram showing this reationship:
http://baby.indstate.edu/gga/gga_cart/barycen1.gif
Look here for a more in depth discussion: