The 1862/1 Three-Cent Silver is a popular variety that collectors have known about since 1963, when it was discovered by John Cobb (according to Walter Breen). The overdate itself is weak and appears mainly as a burr extending downward from the bottom of the 2 on the left side. A more noticeable diagnostic is a die break that runs through the 1 of the date, connecting the left side of the star point with the rim.
In terms of rarity, the 1862/1 Three-Cent Silver is roughly three times as scarce as the "normal" 1862, but the overdate commands only a small premium except in the highest grades. Because collectors have known about the variety for such a long time, numerous Mint State examples have been discovered. The most frequently seen Mint State grade is, surprisingly, MS-65. The finest 1862/1 Three-Cent Silvers are a dozen MS-67's certified by PCGS as of December 2011. No Proof Overdates have been seen.
Most 1862/1 Three-Cent Silvers exhibit a strong strike, and some examples show evidence of die clashing (mostly on the reverse, where lines of the shield can be seen around the bottoms of the Roman numeral III).