The 1878-S FS-801 Trade Dollar is a true Doubled Die Reverse, with strong doubling on 420, the arrows (heads and shafts), and lesser doubling on the motto and on some of the legends. In most grades, this variety is worth two to three times that of an un-doubled example. Fivaz and Stanton called this variety: "...very difficult to find in AU and above." The PCGS CoinFacts Condition Census begins around the AU level, but includes seven Mint State examples. The best FS-801 we've seen is the PCGS MS64 from the Concord Collection (illustrated above).
This variety should not be confused with FS-803, which also has doubling on the reverse but to a lesser degree than on the FS-801.