1872-S Half Dimes are found in two major varieties: one with the mintmark within the wreath (below DIME) and another with the mintmark below the wreath. There does not appear to be an official explanation for this difference; rather, it seems that the placement of the mintmark was at the discretion of the die-sinker at the Philadelphia Mint (where the vast majority of mintmarks were added to the diesd before being shipped to the appropriate branch mint). There is ample precedent for the "travelling" mintmark. From 1838-1859, the mintmarks on Half Dimes were placed within the wreath. From 1860-1869, the mintmarks are below the wreath. From 1870-1872, the mintmark moved back to below the wreath, except for the 1872 variety with the mintmark within the wreath. Was a leftover die from 1869 or earlier re-used in 1872? It appears not, as the mintmark in 1872 is a different size and shape from that on the 1869.
According to the PCGS Population Report, the Mintmark Below variety is approximately 3.5 times more common than the Mintmark Within variety. The most commonly seen grade is MS-64, followed by MS-63, then MS-65. Gems are scarce but not unreasonably so. MS-67 examples are very rare and the finest example certified by PCGS (as of May 2011) is a single PCGS MS-67+.