Pests

Owls
The owl, or rather one or more species of owl, was introduced in New New York to wipe out rats and pigeons. While the owls proved largely successful, they themselves replaced both species as the most prevalent pests in New New York. Owls are still capable of flight but feed on trash and have been seen exiting holes in walls, suggesting they live there.

Eradication
Owls are usually caught in owl traps, such as DEF-CON Owl Traps, the operation of which sounds much like a 21st century mouse or rat trap. They occasionally also get caught in spider webs.

Golden Marmosets
Apparently introduced to wipe out other pests, most likely some kind of insect, the Golden Marmoset is a small primate that in the 21st Century still lived in trees. By the year 3000 they wander the streets.

Appearances

 * (mentioned only)

Cockroaches
Cockroaches are still prevalent, some have been seen to be human sized and capable of flying high above the city.

Rats
Despite the introduction of the owl to New New York, rats are still present, albeit with a greatly diminished population. It is fairly rare to see a rat in New New York, unless you live in the sewers, in which case your favourite burgers may have their droppings as an ingredient. On the surface, some now treat rats as birds were treated in the 20th century.

Pigeons
Despite the introduction of the owl to New New York, pigeons are still present, albeit with a greatly diminished population. It is possible they are now purely migratory populations, and may not even be a pest at this point. Like rats, the attempted eradication may have only taken place in certain regions, allowing the animal to return.

Land Squid
As predicted by scientists, the Squid has adapted to life on dry land. The land squid is small and harmless, not much else is known.

Quotes

 * Hermes: Concerning our pest problem: Somebody's been leaving food around and it's attracting owls. And I, for one, am getting tired of cleaning those owl traps. [A trap snaps and an owl hoots.]