These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ensemble Darkhorse: The Patchwork Girl was very popular when she debuted, but nowadays Jack Pumpkinhead has been gaining quite a bit of popularity.
Fanon: Since continuity and backstory are pretty vague at best, there have been many attempts by fans to make it more coherent. Sometimes an attempt is good enough to be considered good as canon by fans.
Fanon Discontinuity: After the first two books, it's pretty easy to just take your pick of whatever you don't want to consider canon. Baum didn't seem to worry too much about what was canon either.
LGBT Fanbase: "Friends of Dorothy" originated with the gay male fanbase for Judy Garland, and Wicked added another surge, so the original books imported a hefty dose of it. It helps that there's a fair amount of Ho Yay and Les Yay in the main cast, and that Ozma spent her first 15 years or so as the incorrect gender.
Magnificent Bastard: Oscar Diggs. A third-rate Nebraska con man lands in a magical fairyland. He knows nothing of the land or its customs. He is very much a squishy, not very physically stout, Muggle. Yet, within weeks, using a combination of BS and carny tricks, he has bluffed the four most powerful magic users into standing down in an Enforced Cold War, made himself an undisputed God Emperor, and sold the true heir to the throne into slavery, bespelled as the opposite gender! Baum played this aspect down in later books, but modernadaptations certainly have fun running with it.
Mary Suetopia: L. Frank Baum envisioned Oz to be this. Even with Wicked Witches around, Dorothy never had to pay for anything. It gets more explicit in his later books when Ozma assumes the throne and everyone in Oz is granted functional Immortality.
Nightmare Fuel: The Oz books have several instances of this, as does the movie Return to Oz. It's possible to make a complete list of this.
How Princess Ozma was found in The Marvelous Land of Oz might qualify.
Princess Ozma had Bungle's brains changed to make her more agreeable. (May count as Canon Discontinuity as Bungle has her old brains and attitude back in later books.)
The Tin Woodsman's actual origin. Yikes!
And what happened to his original body parts (see below).
Nick Chopper himself could qualify. All he wanted was to earn enough money to be a proper husband to his fiancee. The girl's parents didn't like him, so they went to the Witch and got his axe cursed. He chops off limbs, but is lucky enough to have a tinner just pass by at the right moment to rebuild him with metal. Back he goes to work, because he really wanted to marry her. Eventually, his whole body was rebuilt. Why does he want a heart? So he can go back to his girlfriend! He's okay with the placebo the Wizard gives him, but when he finds his girlfriend again? Well, while he was working his tail off (and losing body parts in the process), she was cheating on him with a soldier who got the same curse. The tinner was likely working for the Witch (seeing as she did him some favors like gluing on a severed finger), and has built Frankenstein-style creations of metal and flesh. And Nick's ex-girlfriend married one that was built from both her suitors' curse-amputated parts!