Mining The Moon

It's a well known fact, that if you stand on the Great Wall of China, you can see the Moon and if you have an especially decent telescope you can now see a small rover with Made In China stamped on the side as China becomes the third country to complete a moon landing.
The rover has made the 225,745 mile trip to carry out a three-month exploration of the surface looking for natural resources.
Prof Ouyang Ziyuan of the department of lunar and deep space exploration explained that one of the main motivations behind the drive to investigate the Moon was to bring back it's resources: 'The Moon is full of resources, mainly rare earth elements, titanium, and uranium, which the Earth is really short of, and these resources can be used without limitation' he said which i'm not sure if i find worrying or not.
The mass of the Moon is 81 quintillion tons, the Earth is 6.580 sextillion tons and they are involved in a celestial dance where the Moon is kept spinning around the Earth by a balance of acceleration and gravity equalling each other.
If we start tinkering with the mass of the Moon by transporting some of its mass back onto Earth, will this have an effect on us and it? 
Taking millions upon millions of tons of the Moons mass would surely, over time, have to have an impact on the Moon's gravitational pull on Earth, creating a change in the seas tides and currents and weather patterns. Would a less dense Moon be slowly pulled towards the Earth or flung out of the gravitational grip we hold over it which would slow the Earths rotation considerably, not to mention the potentially devastating Earth's wobbling effect that the Moon controls.
Maybe mining the Moon won't have any effect, it's too much to get my brain around so i have emailed NASA to get a definitive answer to the question of if we could be creating a problem for ourselves at some time in the distant future.
Meanwhile, congratulations to the Chinese for entering the theatre of Space Exploration and i hope that this is a first step to a manned mission so all the conspiracy theorists can celebrate China being the first country to put a man on the Moon.