The following 1920 Pilgrim commemorative half dollar is believed to be counterfeit. See P7040 and P7050 for die trials believed to be of the same fabric.
On the obverse, the obverse stars and periods are larger and the clasp on the book is stronger. Governor Bradford's eye also appears to be closed. On the reverse, the 92 in 1920 is higher, the position of the bowsprit with relation to the M in PILGRIM is wrong and the configuration of windows is different.
Additional information on these can be found in the January 20, 1988 edition of Coin World.
Photo courtesy of Scotsman Auctions.