Adaptation Displacement: Though it's not entirely Disney's fault. The movie was based on an extremely obscure and unnoticed children's book that was only in print for a very brief time, which Walt just happened to stumble upon at a bookstore and cost him only a couple bucks. In fact, if Disney hadn't made an adaptation of it, chances are Dumbo would literally have been almost completely unheard of today.
Alternative Character Interpretation: In the climax, are all the clowns genuinely terrified of Dumbo flying and panic? Or do some decide to go with the change in routine, like the ones that enter the barrel, because it's their job to entertain? After all, good comedians know when to improvise.
Big-Lipped Alligator Moment: The (in)famous "Pink Elephants On Parade". Acknowledged as confusing or outright Nightmare Fuel to younger or more vulnerable viewers, especially those not understanding Dumbo and Timothy are supposed to be drunk, although is through this accident that Dumbo uses his ability to fly for the first time without knowing it.
Base-Breaking Character: The crows. Some viewers claim that they are a racist portrayal of African Americans and that they are portrayed as unemployed layabouts. Others point out that while dressed stereotypically so that the audience knows they are 'Black', they are the sole characters aside from Timothy who are sympathetic to Dumbo and readily help him. They additionally point out that it is Timothy they initially mock for his ridiculous idea of a flying elephant, ergo standing up to his 'authority'. They are also portrayed as being very clever, a trait not previously shown in stereotypical African American characters. Jim Crow, leader of the crows, is never named on screen and it was just a pun around the studio, this being a nickname for a Black man (the character's real name was Dandy, as in Jim-dandy, a term that dates from at least the 1840s meaning "first rate" or "perfect." It probably originated with Black entertainers).
"Common Knowledge": The lead crow being named "Jim" is commonly used as an example of how problematic the film is... even though he is never referred to as "Jim" onscreen, only in model sheets. More recent official sources have called him "Dandy Crow" instead. The original name was in reality changed back in the 1950s.
Casey Junior. Doubles as Ascended Extra; despite appearing in about four scenes throughout the whole film, he has a memorable theme song (which is among the most viewed Dumbo-related videos on Youtube, even more than Baby Mine and Pink Elephants on Parade), got a book based on how he was purchased by the circus (aptly titled The Story of Casey Jr. by Walt Disney), and got a place in Disneyland as one of the original attractions, making him one of the most iconic characters maybe not just from Dumbo, but between the Golden and Silver Ages of the Disney Animated Canon in general, and thats saying a lot, especially for a Flat Character like him.
Consider that the crows are among the limited number of characters who are at least half-decent to Dumbo, and prove to easily be the most clever creatures in the movie. Though stereotypically "Black" and led by a crow named Jim, they're glad to take a fellow outcast under their wing and help him to get back at his oppressors. With the exception of Cliff Edwards, the voice actors were also Black singers, the Hall Johnson Choir (you can also hear them all the way through The Green Pastures). All of them did a fantastic job on their song. When asked about it, Floyd Norman, one of Disney's first Black animators, defended the characters as saying that they were never conceived as flat racist stereotypes so much as a spoof on popular Black entertainers from the era, and that he personally never saw them as offensive. We like them and more importantly are encouraged to like them. In 2017, Whoopi Goldberg won a Disney Legend award and in her acceptance speech declared that the crows should become regular Disney characters and appear on merchandise; among other things, they sing the most iconic song and that everyone remembers.
"Song of the Roustabouts" portrays Black laborers exploited by the Ringmaster putting up the circus tent. But the lyrics "We're happy-hearted roustabouts", given the downbeat tone of the song, is appropriately passive-aggressive and invites sympathy from the viewer.
Germans Love David Hasselhoff: While the crows are rather divisive and polarizing characters in America, although loved and defended by fans, critics, historians, writers and other personalities, they're very popular in foreign audiences, especially in the Latin American audience, mainly because the visual pun is lost for non-English speaking audiences and, in the case of the Latin American public, because the translation limits a lot of localisms and regional accents in a very clever way. For instance, Jim/Dandy Crow has an Andalusian accent, courtesy of the memorable Florencio Castelló. Similarly, the rest speak in Mexican and Caribbean accents.
It Was His Sled: Dumbo can fly. It's not revealed until late in the film, but the covers feature him flying front and centre.
Memetic Mutation: "Seeing the pink elephants" has been a popular way to describe someone on drugs ever since. Subverted, however, as at the time the movie was made it was already an idiom for someone being too drunk to carry on a conversation with you.
Narm: If you pay close attention during the scene when Timothy washes Dumbo's clown makeup (before "Baby Mine"), a few of Dumbo's offscreen sobs clearly sound like that of an adult.
One-Scene Wonder: The Stork who delivers Dumbo is the reason the Disney crew quickly grew to love Sterling Holloway's voice and he became a regular staple of the studio's work, most notably as Winnie the Pooh.
For the Rail Enthusiast, Casey Junior's iconically catchy musical number coupled with him chugging across the countryside.
Baby Mine., shortly after the previous.
The "Pink Elephants On Parade" sequence.
Dumbo flying, and by extension When I See an Elephant as well as its reprise.
Uncanny Valley: Intentionally invoked with the disturbingly realistic Horus/Illuminati-like eye that appears during the Pink Elephants on Parade segment when the belly dancing elephant dissolves, making this an ironic, nearly-full inverting of the films cartoony style compared to most Disney animated features. Made especially jarring when comparing this to anything else in the film.
"Song of the Roustabouts" portrays Black labourers (Who are literally faceless) putting up the circus tents with lyrics like "we work all day, we work all night, we never learned to read or write" - and a later line "grab that rope, you hairy ape". Even if they aren't intended to be black, the darker colour palette used for the song makes them look black.
There's also the fact that even though the mistreatment of Dumbo and his mother is played for pathos, the movie never questions the system of animals being forced to perform in circuses in the first place. The happy ending just has Dumbo as the new star of the circus. Nowadays, traditional circuses have come increasingly under fire for their animal cruelty and either been driven out of business (e.g. the closing of the Ringing Bros. and Barnum and Bailey Circus in 2017) or phased out their animal acts. This change is reflected in Dumbo (2019), which has an Adaptational Alternate Ending where the circus stops using wild animals, with Dumbo and his mother released into the wild in their native Asia.
What an Idiot!: The bratty kid with the big ears sees Mrs. Jumbo hiding her son, and he decides to go past the rope and tug on his ears. Something like that would have gotten him killed in real life.
Dumbo is openly mocked and given a horrifically insulting nickname from mean lady elephants about four minutes after being born, gets the same treatment from some bratty kids, his mother gets sent to jail for justifiably attacking said kids (not to mention how much worse the attack from a fully grown elephant could have been), he gets relegated to clown duty after getting stage fright on his first big act (which the other elephants denounce him for), and becomes accidentally drunk. He only has one friend in Timothy Mouse to help him get through this, and said friend can't make everything better. When does all this happen? Over the expanse of probably about a week, starting from the day he's born. Dumbo just may be Disney's biggest woobie ever, and you know that's saying enough.
Mrs. Jumbo, whose sufferings we don't get to see, is kept in solitary confinement, unable to defend or even comfort her son through all the degradation he goes through, except for the one time Timothy brings Dumbo to visit her. Even then she can't even see him, only cradle him with her trunk through the bars of her prison. And what would have happened to her if Dumbo hadn't become a star in the end? The best case scenario would be that she's just being confined for observation, pending examination by a vet to make sure she's healthy and was just protecting her child. But in the worst case scenario, she could have been destroyed at the end of the tour.
She's also visibly distraught when the storks seem to have passed her up at the beginning, until she gets a late delivery the next day. Any woman who has miscarried or had difficulty conceiving can relate to how she was feeling.