Ron Guth: The 1851/81 Large Cent is more than an overdate, it is a normal date over an inverted date. When the engraver added the date to the die, he failed to notice that the date punch was inverted. Upon realizing his mistake, he oriented the punch correctly and restamped the date into the die. To efface the error, the engraver ground down the die, resulting in a weak undertype and myriad die lines on the lower and right obverse. The 1851/81 Large Cent is a very popular variety and one which can be detected quite easily.
Mint State examples of the 1851/81 Large Cent are scarce. Most are Brown and most fall into the MS-63 and MS-64 grade levels. Red-Brown examples are very rare and full Red examples are exceedingly rare. The technically finest examples certified by PCGS (as of October 2011) include the following: 1 PCGS MS66 Brown, 2 PCGS MS65 Red-Browns, and 1 PCGS MS65 Red.