Is there an Earth-based telescope that can see the things left behind by the Apollo astronauts on the Moon?

Well, it depends on what you mean by 'see'.

The Apollo astronauts left behind a 1-meter x 1-meter, laser retro-reflector panel, and a ground based telescope in Hawaii used a laser pulse to detect the reflected light from this panel in the early 1970's. So far as I know, it is still being used to determine the precise distance to the Moon to better than 1 centimeter accuracy.

As far as actually seeing anything is concerned, it is impossible to do so from the ground. The lunar landing module launch pad was about 5 meters in size, which from the Earth subtends an angle of 206265 x 5 meters/(384401 km) = 0.0027 arc seconds. An angular distance of 1 arc second, the typical atmospheric limit of any ground based telescope, corresponds to 1.8 kilometers. So forget about locating those Nikon cameras and golf clubs!

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