[lesser_satan]

One thing I worry about: If we removed enough material to significantly alter the mass of the moon, could it affect the moon's orbit, and if so, what effects would that have on tides and things like that?

[Centurion2000]

One thing I worry about: If we removed enough material to significantly alter the mass of the moon

mass of the Moon = 7.36 × 10^22 kilograms

One percent = 7.36 x 10^20 kilograms = 8.11E17 TONS
The bulk density of the Moon is 3.4 g/cc
Estimated 1% of moon's material would be 2.16E23 cm^3.

OR roughly a ball of rock 744km across.

Honestly, I wouldn't worry about it too much for the time being.