If the moon "had" or had had in the past an atmosphere, its gravitational force (about one sixth that of earths) would not have been strong enough for it to stop the gases dissipating into space.
The moon does have an atmosphere but it is very thin, it only has one part unlike earth's atmosphere. The atmosphere of the moon is called the Exosphere. Nothing bad will affect it just more craters...
In fact, the moon does not have an atmosphere. The vacuum of space extends all the way to the surface of the moon. If the moon did have an atmosphere, missions like the Apollo program would not have...
If the moon had an atmosphere, it would have weather just like we do. The footsteps on the moon, which are still there now, would be long gone. Other than that, it wouldn't affect Earth very much/at...