It seems like all we'd have to do, is test whether or not the gravity it exerts on our planet (or anything else) is proportional to the mass we've measured. This would be incredibly easy. Unless of course the moon was composed of something incredibly light towards the core, which we haven't discovered. I think it would be safe to assume that our Moon is strictly composed of what we've gathered. If any other deductions could be made, they probably would have amidst all of the math involved in sending our probes up.
And 4zb41, it is completely implausible for matter in space to gather in the way that would yield a hollow core. Things like that occur due to planetary actions after the fact. If the moon
were to be hollow, and if anything were to "collapse" it, it would be gravity, not a vacuum. And also, I don't think whatever spaceship that would have crashed into Earth exerted enough of a pull to yield a planetoid. If so, earth wouldn'tt be here.