If they didn't change the mass, it maybe okay.
However there are still major issues, for example creating an atmosphere.
Terraforming the Moon is itself a misnomer, as true terraformation would require increasing the lunar mass to be
equal to the Earth’s, something that would be detrimental to life on Earth, and would likely destabilize our twin
planetary system. The correct terms would be caeliforming, and ecogenisis; the creation of a terrestrial
atmosphere, followed by the introduction of terrestrial life. However, although inaccurate, terraforming the term
most people know and associate with the process, and therefore will be used in this article.
Terraforming the Moon presents similar problems to the terraformation of Mars and Venus; like Mars, the moon
would need the substantial increase of atmosphere, and like Venus, it does not have a terrestrial day-night cycle.
However, terraforming the moon, sans the mass/gravity issue, is possible on the same timescale as Mars and
Venus; likely taking longer than Mars, and less time than Venus, to become habitable.
http://www.terraformers.ca/Terraforming-the-Moon.html
Question
Is it possible to terraform the Moon?
Probably not. Our tiny moon has such low gravity that it is very unlikely that any atmosphere conducive to life could be created there. Only the heaviest of gases could “stick” to the moon’s orbit, and even then they would probably dissipate quickly as they break into smaller substituents under constant bombardment of solar radiation. Without tremendous advances in our technology and capabilities, the moon is probably not a good candidate for terraforming. For more information on the moon, check out
http://sse.jpl.nasa.gov/features/planets/moon/moon.html
October 29, 2001
On earth, the size of earth and its core create the van allen belts also that protect us from solar radation.
The moon has a noticeable effect on the earth in the form of tides, but it also affects the motion and orbit of the
earth.
This could really mess with the tides of the earth and the motion and orbit of the earth. Even mining the moon long term and reducing its mass could have detrimental effects on the two bodies gravitational interactions.