When atoms "move", do their electrons generate a net magnetic field relative to the motion? It seems to me that the atoms the make up all the matter on Earth, are always in motion.  The Earth rotates and it revolves around the sun. It also revolves around the Galactic center.  And, we are moving relative to the Andromeda Galaxy.  If all that movement is causing the electrons in the atoms of the world to generate weak magnetic fields, there must be some ambient, net magnetic field around us and around the Earth due to this motion.  If this could be measured, and all the know motions subtracted, would we see a residual magnetic field due to some absolute linear motion through the Universe?  Would that tell us anything about the nature of the Universe and our position in it?  Also, it's seems, this could be used as a navigation tool.  
 A: The key thing you're missing is that all of the electrons in Earth are mixed in with a bunch of protons.  The earth as a whole would have to have an excess or deficiency of electrons for there to be an overall effect.  If you grab two clumps of earth you don't notice any attraction or repulsion, so you know at least the crust is mostly electrically neutral.
A: An easy straightforward test for this idea is to use the fact that in your body, there are $7*10^{27}$, that is seven billion billion billion, atoms, give or take. They do move around inside your body, but the main point is that you personally are not magnetic because the overall magnetic field of all these atoms is zero. 
You can extend that idea to moving bodies such as the moon, which moves very fast compared to a human, but still has no significant magnetic field due to its motion.
The magnetic field of the Earth is, relatively speaking, strong in that it will deflect a compass needle and contribute to the Northern / Southern lights, but that is because the iron atoms in the core of the Earth are moving inside the Earth and are lined up in the same direction, so in this case there is an overall magnetic field.
