The Cozumel Thrasher is possibly extinct in part because the Boa Constrictor was introduced to the island of Cozumel; the snakes were brought to the island in 1971 to be used as props for the filming of the movie, ‘El jardín de tía Isabel’.
Some of New Zealand's "native" bird species might actually be introduced.
The Black Swan may be the best-known example. It was intentionally introduced in the 1860s, but because of how quickly the population increased after that, it is believed that some additional black swans flew from Australia to New Zealand not long after the imported black swans were released into the wild in New Zealand, thus apparently making the black swan a native species in New Zealand. Even so, there is no real evidence of black swans flying from Australia to New Zealand and it is quite possible that New Zealand's black swan population is entirely derived from introduced birds.
The Rufous Night-Heron has a small "native" population in New Zealand that resides along the Whanganui River. The first confirmed record of breeding there was in 1995, which is not that long after Wellington Zoo attempted to create an introduced population of rufous night-herons in New Zealand by releasing three birds into the wild in 1982. The species still existed in captivity elsewhere in New Zealand in 1995, too.
The Barn Owl was first recorded breeding in New Zealand in 2008, when a pair bred near Kaitaia in Northland. The population has increased and spread since then. The barn owl is widely regarded as being native to New Zealand, but the origin of its New Zealand population is very suspicious. Barn owls definitely still existed in captivity in New Zealand, both in zoos and in private hands, until 2007, and there was even at least one person who deliberately released barn owls into the wild in Auckland (the region south of Northland) in the 1990s. In addition, there are records of barn owls that reached New Zealand via aircraft and ships. The New Zealand population could have originated from any of these non-natural means.
The Maned Duck was first recorded breeding in New Zealand in the Tasman District of the northern South Island when at least two pairs bred there over the period of late 2015 to early 2016, but all of the ducklings from at least one of the clutches disappeared. The maned duck has since formed a population in the Tasman District. The population is probably at least partially derived from a small group of maned ducks (3.1) that were first seen in the Tasman District in December 2014. The time of this first sighting does not correlate with the period of post-breeding dispersal of maned ducks in Australia, which is when maned duck sightings are expected in New Zealand, so the New Zealand population of maned ducks may be of captive origin.
The information on the Barn Owls comes from this thread on BirdingNZ: Barn Owl, Palmerston North - Page 3 - BirdingNZ.netThat people were privately keeping barn owls (why?) and that Wellington zoo deliberately released night herons both intrigue me greatly. Love to hear?
Okay, but why do you have the maned duck included in your list under a category that has the following description?Regarding the Australian Wood Ducks, there are none in captivity in NZ and haven't been for decades, so Cassidy Casuar's supposition that the wild ones recently established are escaped birds is without any foundation.
Is that the same as saying outright that the maned duck no longer exists in captivity in New Zealand?There may still be some of the following around but I haven't seen any of them for a long time and it is unlikely any still exist in New Zealand collections (private or public).
Yes, pretty much.Is that the same as saying outright that the maned duck no longer exists in captivity in New Zealand?
Turtle traps set up at Coromandel beach to capture abandoned petsPet turtles were allowed for sale in New Zealand because it was thought the climate was too cold for their eggs to incubate and hatch. However, turtle eggs and hatchlings have been sighted at Cook's Beach.

I just learned recently that the Great-tailed Grackle population in the US and Mexico is introduced. Who knew?
I don't know if it has been said, but there's a free-ranging population of Common Rhea (ca. 500 animals) in Northern Germany.
The Greater Rhea in the Wild of Northern Germany