Reading this post, I have a question. All of this talk assumes that we’re either importing from earth or building on site. Would there be any change if we were to bring our supplies from some where else? Some people have speculated about the possibility of mining asteroids and other space bodies. To ask the question another way, if we covered the moon to the percent the we covered earth’s landmass with materials brought in from a near by asteroid, would that change the orbit of either the earth or the moon.
The crust of the Moon is deficient in carbon and water; if we are serious about colonising the Moon, we will need to import water from ice bearing comets or other objectsand carbon from carbon bearing asteroids; fortunately these objects are fairly common in our solar system.
Eventually, thousands of years from now, we might want to cover the Moon in an atmosphere and oceans, retained by a membrane probably made of polymer.
This material will all need to be imported.
SF worldbuilding at
http://www.orionsarm.com/main.html
the Moon has been hit by fairly large rocks during its lifetime, as you can see by looking at it through a teelscope. That’s what makes all them craters. 
Hasn’t sent it hurtling into the Earth yet. I don’t see how we could import more material than arrives there naturally. As has been pointed out, the Earth and Moon gain tonnes of mass every day.
I have read several posts about mass on the moon. Unfortunately none have mentioned the mining of H3 or taking into account Megatons. What real consideration for using the moon as a base or even as an alternative location. Numbers and suppositions are great for students and lawyers but reality dictates that no matter what our calculators states that there are things more constant. If we are to remove Megatons then we would have to carefully balance it with megatons added. Variation of the moons orbit would cause disturbing affects on Our planet. Affects that if one would pay attention would notice curious alterations in temperature severity of annual rainfall unexpected tectonic plate stress em variations causing changes in wildlife. Any one of these things might be over looked or even artificially stimulated merely by minor changes in larger orbits. If any form of movement is to be available for this world we must take into consideration that even the smallest of alterations have vast effects on the largest of bodies.
Well since 2003, we have indeed discovered water on the moon. We could probably get the carbon from zombies.
Unless you crash land every cargo vessel, which seems . . . expensive, you will have to match the orbit of the moon to a moderately close value, adjusted for the angular rotation for the latitude you choose for your colony. That stuff is now in orbit around Earth in exactly the same orbit as the moon. (And would be, even if the moon wasn’t there.)
So, no matter where you get the stuff, you build your moon colony out of materials that are in orbit around the Earth, exactly in the orbit of the Moon. So, the changes in the Moon’s orbit will be limited to the changes that result from the decrease in the difference between the masses of the moon and earth. I suppose there must be a change, but I am unqualified to asses it. I think it would be a fairly small proportion of the amount that the orbit is changing already from other causes.
Tris
But if we store nuclear waste there, eventually it’ll explode and send the Moon off into interstellar space.