Angst? What Angst?: Throughout the series, but most apparent in The Movie, when Eliza disappears from boarding school on another continent, and no one expresses any emotion other than annoyance at the fact that a child is missing.
Broken Base: Not just among Nickleodeon fans (most of which think this show is the reason why Nickelodeon's programming has gone downhill), but among professional zoologists. Some believe it is overly anthropomorphic and encourages dangerous attitudes towards animals, whilst others think that the anthropomorphism and breaks from reality are justified in order to get children interested about zoology.
Designated Villain: The customs agent in "Chew if By Sea." Admittedly, he's a Jerkass who keeps animals in uncomfortable conditions so it's hard to like him. But the show treats him doing his job (preventing the smuggling of exotic animals) as villainous, in and of itself, as if he's to blame for Eliza bringing Emily the wombat into the country.
Just Here for Godzilla: Many people who have watched the show like to admit that they found the aforementioned Nigel Thornberry to be the best part of the show and wish that he had been the main character instead of the base-breaking Eliza.
Hollywood Homely: Eliza is actually really cute for a pig tailed, glasses wearing nerd. Especially in the later seasons where she lets her hair down and starts wearing more feminine clothing.
Granted, according to the book Not Just Cartoons: Nicktoons, this was more a case of Executive Meddling.
On the other hand, the creators were hellbent on ensuring that Eliza never, EVER had her braces removed, as they wanted it to be a more benign detail about herself in order to make children with braces feel less self-conscious.
Lost in Medias Res: Because there was no "origin" episode, viewers were expected to simply assume that, for some reason, Eliza can talk to animals because of a Shaman and that they had a feral child named Donnie for no apparent reason. While the shaman was at least shown in the introduction, how they found Donnie wasn't explained until a Made-for-TV Movie.
There was an origin episode in the second season "The Gift of Gab" which was a Whole Flashback Episode (and the opening sequence does show how Eliza gained the power to talk to animals).
And a more recent one, also concerning a Nigel Thornberry: combining his unintelligible gibberish from a random episode with a well-known song and then photoshopping his face onto the single/album cover. Blaaaaaarghghghgh.
This tendency has now extended to photoshopping his face onto gifs of scenes from Disney movies; later, this extended to any cartoon character and then even further, to anything that can be readily photoshopped (especially gifs where characters appear normally at first, turn away or hide their face temporarily, and return with Nigel's face). They often vary between Uncanny Valley to outright Nightmare Fuel. Example.SMASHING!◊
Moral Event Horizon: In The Movie, Sloan and Bree's plan to kill a thousand elephants...simply so that they can get the ivory. Later, they threaten to murder Debbie to get information out of Eliza (Bree implies that she actually wants to kill Debbie instead of simply getting information.) And if that isn't enough, Sloan later tosses poor Eliza into a raging river for interfering with his plan.
Never Live It Down: If there's one thing most people remember about this series from their childhood, it's the "Naimina Enkijio" episode, mostly for being Nightmare Fuel incarnate for many kids of the 90s. The fact that it's based off an actual legend doesn't help. Such examples from that episode include; creepy wailing from a Ghost Girl constantly calling Eliza's name, Eliza seeing the Ghost Girl as her reflection in a swamp that supposedly grabs and drowns children, and the general creepy atmosphere of said episode thanks to taking place in dense, dark forest.
Nowadays, the show is best remembered for Nigel's "Blaaaaargh" moment and his "Smashing" face.
The Scrappy: Tyler, Eliza's annoying and haughty cousin, who becomes a main character for part of season 3.
Shane also counts. Not only is he a completely unnecessary Satellite Love Interest for Eliza, but the audience is also supposed to like and agree with him despite the fact that he endangered not only himself, but Donnie and Eliza as well, a toddler and a preteen, respectively, and see him as being in the right when his only concern afterward was insulting Eliza, who was understandably furious at his incredibly reckless actions. And that's just his first episode.
Seasonal Rot: From season 3 onward. The show starts focusing less on the animals and locales, and more about high jinks that just happen to involve talking to animals and may or may not feature Idiot Ball play. For comparison, season 2's "Chimp Off the Old Block" centers on the social structure of chimpanzees, and the show's finale "Eliza Unplugged" in season 5 centers on Eliza struggling to confess her love to a pop star.
Wheelchair Woobie: A character of the week was one. The conflict came from Eliza trying very hard not to seem like she's pitying her just because she's in a wheelchair, eventually annoying her.
The Woobie: Quite a few one-shot animals characters actually. Like the hyena from "No Laughing Matter", Emily the wombat from "Chew if By Sea", the rabbit from "Show Me The Bunny" or Tano the cheetah cub from "Cheetahs Never Prosper".