Why is everyone a) simplifying and b) getting it wrong?
As was mentioned earlier, the gravitational force between two objects is:
GMm
----- = F = ma
r^2
This means two things. 1) It's dependant on both the masses of the objects. Yes, the force on earth between a pea and a cannonball is different. However, if you want the acceleration of the pea (for example), you'll find that the mass of the pea divides through, so the acelleration is dependant only on the mass of the earth, and the distance from the earth. Therefore, ignoring air resistance and assuming dropped at the same height, the pea and the cannonball will accelerate at the same rate. 2) It's dependant on the distance they're apart. However, this is distance between the centers of mass of the objects, and relative to the radius of the earth, you're not going to get a very big percentage difference, even if it is squared, so we can ignore that bit.
On the moon, the acceleration of the object being dropped (pea, whatever) will be different, because the mass of the object it's being attracted towards (moon this time) is different to what it was before (earth). mavity is weaker on the moon, things fall slower there, because the moon is less massive than the earth. A cannonball and a pea on the moon will still hit the moon's surface at the same time, but that time is different to the time it would take on the earth given the same height. You can see this on the youtube video shown earlier.
How is this hard?