The effect on the moon was first noticed in 1968, when NASA's Surveyor 7 lander photographed a strange glow on the horizon after dark. Nobody knew what it was. Now scientists think it was sunlight scattered by electrically charged moon dust floating just above the surface. That fits with data from NASA's Lunar Prospector, which orbited the moon in 1998-99. During some crossings of the magnetotail, the spacecraft recorded big changes in the lunar night-side voltage.

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For years, some who work in police and emergency services (such as doctors and nurses) have anecdotally claimed that full moon nights are busier, crazier, and more dangerous than nights when the moon is dim. This perception may be rooted more in psychology than reality.

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In December 23, 2000 issue of the British Medical Journal published two studies on dog bite admission to hospitals in England and Australia. The study of the Bradford Royal Infirmary found that dog bites were twice as common during a full moon, whereas the study conducted by the public hospitals in Australia found that they were less likely.

Via wikipedia

Many neopagans hold a monthly ritual called an Esbat at each full moon, while some people practicing traditional Chinese religions prepare their ritual offerings to their ancestors and deities on every full and new moon.