The ending mentions over 800 lbs of lunar samples being brought back to Earth prior to Apollo 18 and given to many dignitaries and world leaders, many of those samples have been stolen or lost in the mean time. Lunar-rock-spiders may already be amongst the populace, or hiding amongst regular inert rocks waiting for the right moment...
Or you know, simply crushed under the pressure of Earth's atmosphere and possibly couldn't even move as they would have succumbed to the Earth's higher gravity.
Possible Fridge Tragedy—unless Luna 2, the first probe to arrive on the Moon, revealed something to the Soviets more than a decade before the film's events, the Soviets and their cosmonauts would have had no way of knowing what was lurking on the moon. Tragic because it's implied the Americans, through their shared cover-up, actually had some idea but went ahead anyway.
When Walker and Anderson crash in the Lunar Rover. They're in a field of large boulders. There's some footage of some rocks moving around and then Anderson comes to, and the field is empty. Those boulders, some about the size of small cars, were bigger versions of the little spiders.
Which leads to the question of how big can they get? It's unlikely, but are we sure that's really a Moon up there?