The 1866 Three Cent Silver has the third highest mintage of any date from the 1860's, but that is such a meaningless statement because the mintage of the 1866 is a mere fraction of the mintages of the top two dates (1861 and 1861). Both of those dates have mintages of at least 340,000, while the Mint made only 22,000 of the 1866. In reality, collectors value ther 1866 at nearly the same prices as other date with mintages as low as 8,000.
In general, this date is very well struck, usually with full outlines around the star and with nice detailing of the ribbon and leaves on the reverse. The PCGS CoinFacts Condition Census for this date includes mostly MS-67 examples. A single PCGS MS-68 (from the remarkable Simpson Collection) sits atop the condition ladder.