I think it would be quite supercilious of us to think that the moon didn't effect us...the fact that it's gravatational pull alone has such a vast effects on our tides should give us cause to think that maybe if it can effect somthing as big as that then why not us?
I'm not saying that it is just the full moon that effects us, I believe that all the various different phases of the moon effect us.
As mentioned above, it is pretty well known that if a woman has natural menstrual cycles (without using the pill or any other drug that affects this cycle) then it is almost 100% sure to fall around or on the time of the full moon once it has regulated itself. Which is why you find that a group of friends will generally become synced together, as all women, generally are supposed to be on at the same time.
Now I'm not saying that all severer episodes of mental illness are effected (or even caused) by the moon phases but I think that because of the amount of energy around when the moon is full, they just don't know how to deal with that feeling and then maybe go a bit psyco!!....lol.... but then on the flip side, if the moon is waining then they might feel more depressed etc. which might tip them over the edge!
Also, I know from personal experience with working with the public on a daily basis and with people I see time and time again, you get to find certain correllations between when people feel upbeat and raring to go and when they feel down, lethargic and generally quite blasé about things. I have noticed that leading up to the full moon people are more energetic, full of ideas, inspiration etc. and almost buzzing, but then when it is nearly the new moon (or dark moon) phase, people tend to be a bit more down, reluctant to do things or tired.
Try it, next time you feel like your just bored with no reason why, just bored! or if you feel down and you don't know why....find out what the moon is doing and I bet it's waining!!