I would have mentioned this but if I remember right it's hadith not quran. Anyway, my thoughts on the matter:
Muhammad splitting the moon. Now this I can't prove to be false, but I can weight it against other things. People throughout the world at this point gazed at the stars. The Greeks, the Romans, the Chinese, they all had wonderful astronomers who mapped out the night sky. Certain claims by one society are matched by claims in another. Ancient Greeks for example would leave records of things they observed, shooting stars, eclipses, things that would last seconds or minutes, the same claims found with other peoples they had no contact with. Both recorded things matched by the other. So it's reasonable to assume that if Mohammad split the moon and then joined it together again, someone somewhere would have also noticed apart from a few Arabs in the desert. Maybe the rest of the world was on holiday, but I doubt it. I have to say this isn't true.
NASA released a statement on the moon spiting miracle which denied any such event.
http://sservi.nasa.gov/?question=evidence-moon-having-been-split-two