A face only a mother could love: The Cuban solenodon is one ugly critter.
TAKAHE
With its striking green and blue plumage and large red beak, you'd think it would be hard to lose New Zealand's takahe (Porphyrio hochstetteri). But over-hunting and introduced pests reduced the takahe's numbers so severely that it was thought to be extinct by 1900. But in 1948 Geoffrey Orbell, a doctor and keen bushwalker, found a colony of the birds in the remote Murchison Mountains, in the South Island's Fiordland. They are still vanishingly rare, and New Zealand's Department of Conservation estimates there are only 130 takahe in Fiordland, with another 60 in colonies established on predator-free islands.
LORD HOWE ISLAND STICK INSECT
At up to 12 cm in length, the Lord Howe Island stick insect (Dryococelus australis) is a pretty big bug to lose. The jumbo species was once abundant on Lord Howe Island off the NSW coast, its only known habitat. Once black rats were introduced the bug's days were numbered and the last was thought to have died by 1935. Then, in 2001, scientists found a tiny colony of the flightless insects living under a single bush on Ball's Pyramid, a 550-metretall volcanic pinnacle jutting out of the ocean 23 km from their original island home. Thanks to a breeding program at Melbourne Zoo, more than 400 exist in captivity, and there are plans to one day reintroduce the species to Lord Howe Island.
CUBAN SOLENODON
The Cuban solenodon (Solenodon cubanus) hadn't been seen since 1890 when it was rediscovered in 1975. It is one of the world's few venomous mammals. Samuel Turvey, a conservation biologist at the Zoological Society of London, in Britain, says that, while no one knows exactly how potent solenodon venom is, it can kill mice and perhaps even the solenodons themselves, as animals have been found dead with no apparent fatal wounds after fighting.


Judgmental, aren't we?
I take issue with your describing some of these creatures as ugly. While convenient as an adjective, to call a creature "ugly" is to detract from its worth. I have viewed an artist's sketch of a coelacanth and you provide a picture of the solenodon, and I found neither creature ugly. Perhaps you could choose more descriptive adjectives, like "oddish", "timeless" or "shockingly strange".
My first thought was ,
"What the heck am I looking at?"
I had to find images elsewhere, including the same image, but including the other half of the critter and a bit more visual context. Doesn't strike me as particularly ugly, but I don't think the author was doing anything other than being playful. If there is anything other than that behind the "ugly" description, my response then is, "Pfft. Whatever."
Ugly Animals
I also tried to come up with some other "polite" adjectives for them (unique? surrealistic? gnarly? lifeforms with fun-personalities? ... ), after seeing the word "ugly" repeated in the story.
Alas, I finally couldn't help but agree with the author. Those critters are UG-GLY! Sorry.
Strange, but could that be why they survived? No ancient predator found them especially appetizing looking. ;-)