Ron Guth:
It's time to revisit this date in light of modern research and opinions. As David Akers noted, the "overdate" on the 1802 Quarter Eagle is indistinct. Harry Bass questioned whether this was an overdate at all, and John Dannreuther (co-author with Bass on "Early U.S. Gold Coin Varieties: A Study of Die States 1795-1834") called it a regular 1802. PCGS recognizes the variety as 1802/'1' with single quotation marks around the 1, indicating its questionable status. I suspect that in the future, this nod to tradition will be removed, consistent with Dannreuther's treatment.
This date is scarce, plain and simple. However, ample supplies exist in most grades to satisfy collector demand, which comes primarily from type buyers. In Mint State, this date is very rare, though the PCGS CoinFacts Condition Census consists of all MS63 or better examples. Two NGC MS65 examples appear to be the best exmples of this date.
Most 1802 Quarter Eagles show central weakness at the centers and on the reverse stars. Adjustment marks can be seen on the occasional example, but they appear to be the exception rather than the rule.