The Wild Thornberrys/Headscratchers

Why couldn't Debbie have gone to boarding school?

Yes I know her grandmother (rather harshly if you ask me) dismisses her as "too far gone" in the movie but why not? Maybe I just sympathise with her despite her position as Bratty Teenage Daughter and think there's something wrong with her parents dragging her all over the world when she obviously hates it. Nigel's certainly rich enough to send her to a private boarding school or do they care more about having a babysitter than their daughters feelings? I'm not saying Debbie isn't unduly whiny or anything (even though I really like her) but I can understand why she hates it, animal activism doesn't interest her and she doesn't get to socialise with other teenagers at all.

I think there was one episode of the cartoon series where she tried and failed the interview. And despite her complaints maybe Debbie feels being closer to her family is better than being in a boarding school.
The latter may actually be true, but I can't help but think there would be a boarding school out thre which would waive the interview and just let her in to say they had the daughter of a famous animal expert attending. Actually, surely a lot of private boarding schools will just let the kid in so long as their parents can pay.
She passed the interview in the episode where she decides to go to boarding school but the Aesop is about how families always stick together and you love your sibling deep down no matter how much you fight, so she decided not to go.

In the Crossover with the Rugrats

Toward the end the babies sink the submarine and can't surface because they've run out of fuel. Why not just empty the ballast tanks?

Because the pressurized air kept to force water out of the ballast tanks is used only for the last bit of distance needed to bring the periscope-depth sub above the water line. Pumping water out of the tanks at deeper depths requires the engines.

Eliza made the stupidest wish imaginable

Shaman: "You have saved my life. I will grant you a wish in gratitude." Eliza: "I wish that I was an omnipotent God-being that could be anywhere and do anything at the speed of my thoughts."

Think of the untold power she had in her hands. She could have wished for a cure for AIDS, or peace in the middle East, or any number of things to benefit all mankind. Instead, she became Dr. Dolittle.

It's just a kids' show...
Most likely, the Shaman couldn't have granted a wish like that. At first, he couldn't even give her the "gift of gab" without taking away her ability to talk to people. She was only able to talk to both after he gave her the "deluxe spell"--which he wasn't even sure was going to work. Shamans are people too, and they can only do so much.
- Exactly, he's a shaman, not a god.
She's, what, twelve? If you found a genie or something as a preteen, would you have wished for a cure for AIDS? Did you even know what AIDS was? Eliza likes animals. Her wish makes sense from the perspective of someone her age.

Eliza shared her secret from the very first episode.

This doesn't so much bug me as it amuses me, but when Eliza narrates to the audience at the beginning of every episode, she says "and between you and me something amazing happened! Now I can talk to animals! It's really cool, but totally secret." You just shared your secret with us, Eliza. Now you've lost your powers.

Perhaps it doesn't count when you break the fourth wall.
The weird thing is they never really mention that she can't tell anyone about her powers until they air the episode showing her getting them. I think they added it in afterwards to Hand Wave her not telling anyone.
Perhaps she writes in a journal or diary or something? Something that tends to crop up in kids shows is a character writing a journal writes it as a series of letters--Doug being a prime example. So she's not actually telling anyone, we're just hearing her journal entries. Or she has an audio journal. Something like that.

Kip and Biederman

Something struck me as slightly odd while I was watching the Vacant Lot episode. Eliza discovers that Kip and Biederman are ravaging the rainforest and amasses an army of animals to fight against them and destroy their machine. Wouldn't they consider it more than a little oddthat she was able to command them in the first place? Biederman has the excuse of being a complete idiot, but Kip should have seen that something was up.

We may as well ask why her family never caught wind of the fact that Eliza could talk to animals. There have been plenty of episodes where the animals ran in to save their butts, led by their dear lil' pumpkin where, by using logic, this would never have been possible unless...She somehow managed to communicate with them! So, in a way, they are all being stupid for not seeing it.
Why do they always seem to be where the Thornberries are? You'd think either Kip would go: "wtf?! U chasing us or something?" or Mrs. Thornberry would file a restraining order against them?

Donnie

I never really understood Donnie. Was he supposed to be a Shout-Out to The Jungle Book or Tarzan or something? Why didn't Eliza try to talk with him like she would the other creatures? Why and how did the family find him?

I'm uncertain as to what the inspiration behind Donnie was, but it's clear he was at least meant to be an archetypal "Wild Child." There was never any evidence shown of Donnie actually knowing animal language, so it's unlikely that Eliza could communicate with him with her powers. As for his origin, there's actually a massive special devoted to just that.
- Be sure to have tissues on hand.