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Model X Video & Photo links from First Public Intro at Santana Row, 3/16-18/2012

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It sounds to me like you were merely holding the camera in such a way that you were smothering the microphone. You can see that the audio becomes muffled (or restored) as you change your grip on the camera. And when muffled, the clicking sound is the autofocus and/or aperture mechanism -- made very apparent by blocking external sound. So, it's avoidable. You just need to be more careful in how you hold the camera. (Don't blame the innocent ! ;-)

Thanks, Incredulocious, for figuring this out! Glad it was operator error and not my camera. (I would have replaced it already with an iPhone 4S which shoots 1080p HD video. However, I'm not upgrading my iPhone until the iPhone 5 comes out supporting 4G LTE, like the new iPad does.)