.: Entry and Exit from the Moon
For this to work, there needs to be a mechanism that will allow the particles of people and objects to shift from our matter to mirror matter and vice-versa. Whenever someone arrives on the island accidentally, they first endure some sort of electrical storm. So we'll assume that anomalous electromagnetic fluctuations while the moon is passing by you on Earth are capable of shifting your particles.
[Since the Others seem able to come & go, recruiting Juliet etc, there must also exist] Controlled means must for shifting.
The sub seemed capable (if Locke shifted the sub while the sub was in the ocean in our world and the hatch was open, he would've been soaked). and he was?* in epis The Man from Tallahassee. hmm. so is this suggesting - 'if Locke shifted the sub - that Locke left the island (the mirror matter universe) and shifted back into our world, then shifted back again, all before walking down the dock leaving the sub (at least seemingly) to explode behind him?
The Looking Glass would be a target for sub alignment. Line up the sub in one of our oceans, wait for the short window, and shift to the moon pool. the pool within the Looking Glass. The materializing sub is hidden from the naive residents of the DHARMA initiative.
Likewise, controlled entry by parachute would make sense if you are able to shift while aligned with the atmosphere of the moon.

*Wrap-up: Why might this work? huh this "why might work" sxn no longer there. there last nite, gone today. glad I excerpted it.
... it can explain minutia, like the need for parachutes and a sub, how Naomi's story could have a semblance of truth, daylight before the crash, Locke getting wet in the sub...