“The most mysterious of all the Pacific waterfowl is Coues’ Gadwall, Anas strepera couesi, only two specimens of which have ever been found, on Washington Island, more than six hundred miles south of Hawaii. The two specimens, the male type and a female, collected in 1874, are now in the U.S. National Museum in Washington. In appearance these birds are simply Gadwalls reduced to about two-thirds normal size. The plumage too is rather dull and somewhat unfinished-looking. Washington Island is a marshy place only a few miles long, with a small brackich lake near the centre and a fringe of palms. Since he original pair of birds were discovered, several expeditions have stopped at the island, but no one has ever seen Coues’ Gadwall again. Speculation is perhaps unprofitable, but sometimes it is irresistible. I often like to wonder how these birds ever came to Washington Island. It is my guess, for what it is worth, that these two specimens represent the last of a very small inbred breeding population of true Gadwalls which by an accident of migration had become established on the island. I suspect that their size and coloration are due to environment and inbreeding rather than to any genetic change.“ 
This account summarizes quite well what’s known about this bird.
Then there are some strange accounts, or rather misinterpretations of accounts, let’s start with one that is rather less known, and speaks of the occurence of a form of gadwall on the Society Islands.:
“Forster met with a species of Gadwall on the Society Islands and identified it with A. strepera Linn. It is much more likely that is was C. couesi, for the range of that species doubtless extends beyond Washington Island, the only locality as yet known for it.” 
I read this original account by J. R. Forster, which is completely in Latin, and which merely is a enumeration of species, the duck is mentioned here just as “Anatem streperam“, that’s all, and this account almost for sure refers to the Pacific Black Duck (Anas superciliosa Gmelin), which occurs on the Society Islands, and which is not separately mentioned here … and in fact, Forster mentiones “Anas strepera” again in an enumeration of birds he describes from New Zealand, this also clearly refers to the Pacific Black Duck! 
Then there’s another account in a German book, which again is refering to an account in James C. Greenway’S “Extinct and vanishing birds of the world” from the 1960s.:
“Interessant ist eine weitere Bemerkung desselben Autors, wonach nach Angaben von Ripley ein auf den Tuamotu-Inseln gefundenes Entenkücken sich bei Erreichen der Geschlechtsreife als Schnatterente herausstellte.”
“Interesting is another comment of the same author [J. C. Greenway], based on which according to Ripley a duckling found on the Tuamotu islands, when reaching maturity, turned out to be a gadwall.” 
Okay … after purchasing J. C. Greenway’s book, which took me ages again, I can now proudly present you this abovementioned account by the ominous Ripley.:
“But, on the other hand, Dr. S. Dillon Ripley tells me that a duckling taken on the Tuamotu Islands was raised by Charles Nordhoff at Tahiti. When it reached maturity it turned out to be a gadwall.” 
That’s all, we actually deal with hearsay, an account of an account of someone who claimes to have caught a duckling on one of the Tuamotu Islands (these are actually the largest island group in the world consisting of no less than 76 atolls, just by the way ….) without naming the island in question.
However, given the geographic position of Washington Island/Teraina, a former occurence of this bird on the Tuamotu Archipelago makes much more sense than on the Society Islands.
But now let’s take a look on what these two persons, Dr. S. Dillon Ripley and Charles Nordhoff, have to tell; we start with Mr. Ripley …:
“It sometimes happens that migrating Ducks plummet down on to isolated islands in the Pacific. Mr. Charles Nordhoff told me once that a schooner captain inbound to Tahiti from Flint island, an isolated rock pinnacle three hundred miles or more north towards Hawaii from the Society Islands, brought him a duckling which he had picked up on the island. Mr. Nordhoff was able to raise the bird, and found that it was a Pintail, presumably from wild parents. If Pintails can fly so far south of Hawaii where they are in the habit of wintering, there seems no reason why Gadwalls should not be able to do the same thing.” 
… and go on with Mr. Nordhoff.:
“In his article in the Waterfowl number of the AVICULTURAL MAGAZINE, Dillon Ripley mentions a duckling I received some years ago from Flint Island, which when reared proved to be a fine male Pintail. I believe that a good many stray Ducks from the Northern Hemisphere land on the Pacific Islands, and occasionally, as Ripley suggests in the case of Coues’ Gadwall, give rise to a sedentary and eventually inbred race. I have reliable information that Shovelers in winter plumage have vistited both the Marquesas and the Tuamotu on several occasions, and that Pintail have been seen on Atiu in the Cook Group, south-west of Tahiti.” 
Well, well, so the Tuamotu Islands suddenly has changed into Flint Island, which in fact is not a part of the Tuamotu Archipelago but of Kiribati – and – the duckling that was supposed to turn out being a Gadwall was in fact a Pintail (Anas acuta L.), a completely different species of duck!
After all, we are left with probably more questions than answers.
 Johann Reinhold Forster; Hinrich Lichtenstein: Descriptiones animalium quae in itinere ad Maris Australis terras per annos 1772, 1773 et 1774 suscepto. Berolini: Ex Officina Academica 1844
 Lionel K. Wiglesworth: Aves polynesiae: a catalogue of the birds of the Polynesian subregion (not including the Sandwich Islands). Berlin: R. Friedlaender & Sohn 1891 In: Abhandlungen und Berichte des Königl. Zoologischen und Anthropologisch-Etnographischen Museums zu Dresden Bd. 3: 1-84. 1890/91. herausgegeben von Hofrath Dr. A. B. Meyer, Director des Museums
 Charles Nordhoff: Notes on the birds of Tahiti. The Avicultural Magazine ser. 5. 8(5): 119-120. 1943
 Dillon Ripley: Pacific Waterfowl. The Avicultural Magazine ser. 5. 8(3): 67-70. 1943
 James C. Greenway, Jr: Extinct and vanishing birds of the world. Dover Publications, 2nd Edition 1967
 Dieter Luther: Die ausgestorbenen Vögel der Welt. Westarp Wissenschaften 1986