|MadSci Network: Astronomy|
I'm glad to hear that people aren't taking the Fox News show very seriously! For a very effective critique of the program, see Phil Plait's Bad Astronomy Page. I didn't see anything about this particular issue, but there's lots more information that you'll probably find interesting.
Anyway, we do not now have any optical telescopes that could image small objects on the moon. If we assume that the leftover equipment is about 10 meters across (probably not bad for an order of magnitude estimate), the equipment would have an angular size of about 5 thousandths of an arcsecond at the earth's surface (or in low orbit). An arcsecond is 1/60th of an arcminute, which is in turn 1/60th of a degree - very, very small! Because of turbulence in the atmosphere, ground based optical telescopes currently only get a resolution of about half an arcsecond; the Hubble Space Telescope gets a resolution of about 0.1 arcsecond.
Astronomers are currently talking about building large telescopes with diameters up to 100 meters. Assuming that they could correct perfectly for the atmospheric turbulence (using a technique called adaptive optics) such a telescope could see objects this small on the moon. But this is at least 20 years away - probably more if we are to correct for the atmosphere so carefully. Another possibility is to put a 20 meter diameter telescope in space - but there are currently no plans to do that, as it would be extraordinarily expensive (it would have nearly 100 times as much glass as the Hubble!).
Try the links in the MadSci Library for more information on Astronomy.