Apollo landings, 11, 14, and 15 left 'corner reflectors
' on the moon. They are basically big mirrors that are sitting on the moon, so that we can bounce lasers off of them. They are actual physical objects, that can be objectively verified by anyone with a laser powerfull enough to send a signal to the moon. This is the system that we use to determine the exact distance of the moon from the earth.
(you aim the laser at the moon, and since the moon is about a light second away, you get an echo back.)
In 2008 the LROC
is supposed to be doing a site survey for various reasons. Problem is that it's also difficult to verify for average people. The largest peice of hardware on the moon is about 20ft across if I my notes are correct. This means that most telescopes are not going to be able to see them.
However, if you go to http://moon.google.com/
you'll discover something very interesting at the highest magnification.
As for the radiation, she's probably thinking of the Van Allen belts.