ABC News has an article with everything you ever wanted to know and more about the belief that full moons cause behavior change, particularly in chaotic and destructive ways. It cuts through the history of the belief and points out that law enforcement and medical workers hold these beliefs stronger than other, despite the fact that data does not indicate any change in problems when there is a full moon.
I think this is one of the best examples of misattribution of behavior that exists. For many people, if something strange happens on a night that there is a full moon, the incident or behavior is attributed to the moon, reinforcing this belief. However, the same people fail to notice that when the exact same situation happens without a full moon, the moon is not even thought of as a possible reason.