WMG / The Wild Thornberrys

Nigel Thornberry is a Time Lord
His strange behavior is because he's unfamiliar with the customs of 20th-century Earth, and he got a job hosting a nature show because he was curious about the "exotic" wildlife of Earth's distant past—naturally, the Commvee is a disguised TARDIS. He probably secretly had a hand in Eliza getting her animal-talking powers through some kind of sufficiently advanced technology, because he knew that it would make the job a hell of a lot more interesting.

Donnie has similar powers to Eliza
  • He never seems to have trouble understanding Darwin or other animals Eliza talks to. Also notice how when we see Darwin interact with anyone other than Eliza he speaks his chimp speech (including other animas) yet he and Donnie have been alone together many times and he addresses Donnie the same way he addresses Eliza.
    • Also Donnie seems to be aware of Eliza's powers, but she is still able to keep them. Maybe the rule doesn't apply to others who can talk to animals?

Eliza awakened her Jacobson Organ just like in ReGenesis
In the Cannadian TV series ReGenesis one of the protagonists, Dr. Bob Melnikov undergoes an optic nerve reconstruction using a virus and awakenned his Jacobson Organ that gives him the ability to "feel" the other people feelings through the Pherormones. But... in real life, the Jacobson organ is important in the social aspect of animals and their way of comunicate. So... the Shaman or someone else reactivated Eliza's Jacobson Organ in some way and then she gain the ability to talk with animals: She feels the pherormones and her brain "translates" this smells to words.
  • But in Regenesis... Dr. Melnikov awakenned his Jacobson Organ with an HSV-1 virus... so that mean that the Shaman or any other, awakened her Jacobson Organ in a very disturbing way.

Debbie will grow up to be an anthropologist of some sort
She finds animals boring, but as much as she complains about the world trip she really quickly makes human friends and often adapts well to other human cultures. I honestly think she may become an anthropologist or something similar, maybe even a documentary maker like her parents but about other people and cultures and not animals.

Eliza has a brain tumor, and the whole series is made up of her coma dreams.

Eliza is just pretending she can talk to animals to cope with loneliness.
Eliza is pretending to talk to animals, in a way similar to having an imaginary friend. She doesn't get to talk to many kids her age, so it's just a way to deal with her family's lifestyle. Notice how she gets really excited to be around any kid her age, and how the animals she talks to tend to deal with the same problems she is dealing with.

Nigel Thornberry is actually the love child of Megatron and Matthew Patel.
You read it here first people...

Mary Ann had long hair in high school.
In the shark episode, she mentions watching a movie about a man-eating shark as a teenager. Jaws would have been the big summer blockbuster of the time. A friend mentioned Mary Ann looked a lot like Christie, the shark's first victim. (May have meant it as a complement as she was an attractive young lady.) Mary Ann was just creeped out watching someone who looked like her get eaten alive, so she cropped her long blonde hair in order to look less like her.

The series is a drug-induced hallucination by some animators at Klasky-Csupo
That explains Eliza talking to animals and Nigel Thornberry's fucking face. The last thing they saw was some concept art for the show.

Donnie knows about Eliza's gift...and he isn't the only one
There's a loophole in play with the Shaman's gift, you see. He said Eliza couldn't tell people about her ability to talk to animals. He never said that people couldn't figure it out on their own. Donnie has been shown to be more observant than he leads on, so he may well be aware of Eliza's gift and since he can't talk yet is able to keep her secret easily. Lending support to the latter half of this guess, Debbie implies that she at least suspected that Eliza could talk to animals before the actual reveal.