Dumbo/WMG

The Pink Elephants Are Poltergeists
Normally, they are shy, nomadic spirits that roam the lands, usually keeping to themselves, unless they come across a person who is too mentally unsound (i.e. drunk) to strongly react to them, and thus begin their fun. While these creatures are shapeshifters, they have an odd preference for the form of pink-colored Pachyderms.

The kid who taunts Dumbo was teased for his own ears.
There's really nothing in the film to support this except a case of Fridge Brilliance; imagine you're a funny-looking kid with big ears, and all your friends tease you about it -- not exactly a case of All of the Other Reindeer, as they still hang out with you, but they never miss a chance to take a shot at you for it. Your ears reach "meme" status among your peers, and they make a running gag out of teasing you for your big ears. Then, you have the good fortune of seeing an elephant with HUGE ears. You immediately pick up on a chance to divert attention from you, and you point out the ears of the elephant. Some of the insults he uses might even be some that he heard from his friends. Now, whenever the other kids say "you have big ears", you can say "at least they're not as big as that one elephant's". The joke loses its humor, and dies out, and you're free of ridicule.

That wasn't champagne the clowns were drinking.
So let me get this straight. A not even full bottle of champagne (around 12% alcohol by volume) gets diluted by an entire tub full of water, and a mere couple of gulps of this mixture is consumed by a creature with the mass of a baby elephant (probably around 260 lbs). And he almost immediately goes into what appear to be the final stages of delirium tremens. No freaking way. Those clowns had to be knocking back something a lot stronger than that. That stuff was spiked with LSD or mescaline or something.
 * Absinthe, perhaps? I've heard it be called the strongest drink there is. That could account for still being fairly strong even after dilution.
 * Alternatively, maybe it wasn't just water in that tub... I can see an unethical circus sedating the animals to make them easier to manage.
 * Perhaps that tub of water was intended for Dumbo's mom, to keep her docile? Seems they'd need something pretty strong to keep a "mad" elephant under control.

The stork that delivered Dumbo was a replacement stork
The original stork that was supposed to deliver Dumbo to the circus drank on the job one too many times and lost the elephant. When catching up to the rest of the flying V of storks, it got in trouble for losing the baby (and replacing it with Bugs Bunny), Long story short, the original stork was fired and a newbie stork was tasked to deliver a baby elephant to a moving train.