Working in as a psychiatric nurse on night duty for the last 24 years, the myth of the full moon is often discussed.
Everybody says its bad, just like Friday 13th. Ooooooooh, spooky!

Interestingly, the words lunacy and lunatic come from Latin, "lunaticus", which means "of the Moon" Or "Moonstruck"

Also don't forget all those great old werewolf movies.  What triggers this ferocious creature? You got it. The Full Moon.

And remember the human brain is partly protected by sitting in fluid.
Now if you've ever noticed the Moons gravitational effects on water...there could be something the the myth.
But that would mean people go crazy every day as the Moon passes close by on it's eliptical orbit, not just full Moon.