I just did a quick Fermi calculation of the photon density at the eye
after reflection from the retro on the moon. Assuming a beam
spreading angle of 10^(-5) radians, an area of the retro of 1 m^2,
and of the pupil of 10^(-5) m^2, and the laser being a 5 mw green
laser. Assume no losses in passing through the atmosphere (twice).
Stick all that in and you get 10^(-9) photons/sec arriving at your
eye after the round trip from you laser via the retro. So even if
there were a million lasers pointed at the same retro (no mean task,
as David has pointed out-the beam at the moon will cover only about
10% of the moon's disc in my calc., and of course this has to be done
during new moon, so you can't aim it by sight), the photon density at
your eye would be no more than 10^(-3) photons/sec, and you would
have to wait about 10 minutes before you had a reasonable chance of
intercepting *one* photon.
As for reflection from the rest of the moon's surface, we are talking
orders of magnitude lower than this, so the odds of "illuminating the
moon" seem to me to be vanishingly small. I think I'll have to add my
voice to those who say the effort is futile (although it *would* be
neat if it worked, in spite of all).
IIRC, NASA uses a high-powered, well-collimated laser and a rather
large telescope to detect the reflections it gets from the lunar
retro, and still gets a very tiny signal in return for its efforts.