Data from the Mars Orbiter Laser Altimeter (MOLA) and Mars Orbiter Camera (MOC) instruments aboard the Mars Global Surveyor (MGS) were used in a detailed search of a selected part of the South Polar Layered Deposits (SPLD) for impact craters. Impact craters with diameters from 0.8 to 5 km were identified from a MOLA-derived shaded relief map and were primarily validated using individual MOLA tracks and, in select cases, MOC narrow angle images. The resultant crater population determined in this study is at least four times the density of the crater population previously recognized. From these new statistics, we estimate the mean apparent surface age of the SPLD to be 30--100 Ma, depending on the established production model isochrons used. All of these craters are considerably shallower than other Martian craters in the same diameter range. We attribute this shallowness to be the cause of the lower detection rates of previous studies. There is a correlation between crater depth and rim height, which suggests that both erosion and infilling have affected the crater forms. A similar study of the north polar layered deposits uncovered no craters in this diameter range. A limited population of craters smaller than 800 m was uncovered in higher-resolution MOC narrow angle images. These do not appear to have been degraded to the same degree. This separate population implies a surface exposure age of only 100,000 years and perhaps indicates an event that erased all small craters and degraded and infilled the larger ones.