I don't have the patience to look into this or most conspiracy theories, because they fall under the 'tinfoil hat' umbrella.
I will say that the 'two light-source' thing (correct me if I'm wrong), but the Earth would reflect light. If the Moon is at a right angle to the Earth relative to the Sun, it would have two sources of light -- the Earth (reflected) and the Sun.
The most important thing to me when thinking about any conspiracy theory is motive. Sure, there was a space race during the Cold War. But would that be enough for NASA to fake a Moon landing?
In addition, would NASA/the US Government even have the ability to keep the secret contained? What of the people in mission control; those who prepared the event; their families... would they all be able to keep such a secret?
Think about 9/11 conspiracies.
Motive? None, really. You could say 'to start a war', but war is really in no government's interest (in a democracy, at least).
Able to keep a secret? How do you pack a building full of explosives without anyone noticing?
EDIT: The flag. I heard the sides had springs in them. Springs would move in a rather unrestrained fashion on the Moon, with even the lightest touch setting them in motion for quite sometime (low resistance). Thus, 'flag waving'.
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