Can the HST capture images of items left by the moon landing (Apollo) mission?
No, Hubble cannot take photos of the Apollo landing sites. An object on the Moon 4 meters (4.37 yards) across, viewed from HST, would be about 0.002 arcsec in size. The highest resolution instrument currently on HST is the Advanced Camera for Surveys at 0.03 arcsec. So anything we left on the Moon cannot be resolved in any HST image. It would just appear as a dot. The largest sized objects left by the Apollo missions are about 4 metres across, and as viewed from HST, would be about 0.002 arcsec in size (this is the angular width of the side of a 20c piece viewed from 200 km away). The highest resolution instrument currently on HST is the Advanced Camera for Surveys at 0.03 arcsec (this is the approximate angular width of the face of a 20c piece viewed from 200 km away). So anything we left on the Moon cannot be resolved in any HST image and is therefore not detectable.