All major mint errors on U.S. Gold coins are very rare. Very few pieces escaped the quality control at the Mint since all Gold denominations are examined very carefully.
There are only a few known double struck (or multiple struck) U.S. Gold coins. Off-center strikes are also extremely scarce. This spectacular $20 Liberty Gold Piece is the only off-center known. It was struck 15% off-center and certified MS 63 by PCGS.