Ron Guth:
BG-776 is another of the Liberty Head Octagonal Quarter Dollars made in Period Two (1858-1882). In preparing the die, the engraver punched the date into the steel as 7874, mistakenly using a 7 punch for the 1. Upon noticing his mistake, the engraver corrected the error by hand-engraving a misshapen 1 over the first 7. On the reverse, other engraving arrors are noted: in an attempt to finish the second L of DOLLAR, the engraver slipped with his tool and left two long lines running down and to the right of the second L and from the left side of the A.
In the Breen-Gillio reference, this variety is listed as a Low Rarity 5 (about 60 to 75 known), which is consistent with the PCGS Population Report totals.