Chitty Chitty Bang Bang/WMG

Jeremy is James' grandfather and Jemima is Matilda's grandmother.
Everything Roald Dahl has written is part of a Verse. And it is awesome.
 * Except that Roald Dahl didn't write the book the movie was based on, he only adapted it. Ian Fleming did. Think about that one for a bit.
 * Again, everything Roald Dahl has written. The screenplay is something.
 * Obviously this means that everything Roald Dahl and Ian Fleming have written belong to the same Verse.

Jeremy is Q's father.
Q visited his mad old Grandfather's home many times as a boy, and took inspiration from him to get into mechanics; it was his great-grandfather who inspired his foray into Military Intelligence.
 * Desmond Llewellyn, who played Q in every Bond movie from From Russia With Love to The World Is Not Enough plays Coggins, the junkyard owner who sells Potts the old car that becomes Chitty.

The Baroness Bomburst of Vulgaria is a Vampire, albeit one that can stand sunlight.
Having snared the Baron in his youth, she's been draining royal blood on a nightly basis ever since their courtship. Hence his hefty body shape, to keep her satiated; hence her youth and beauty compared to his elderliness; hence his seeming regression to a child-like state, having had blood drained from his brain; hence his pathological desire to murder her; hence her seeming immortality; hence the Vulgarian court's predilection for men dressed in smart black suits. Her pathological hatred of children is due to their purity, their ability to spot vampires a mile away, and of course the toy thing.

Chitty Chitty Bang Bang is (or later will be) The Ghostbuggy.
Bat-shaped wings, amphibious mode, a mind of its own...not to mention its red paint-job.

Caractacus's story actually happened.
After the events in Vulgaria, the main characters simply returned to the beach for another day of fun and frolicking. They aren't fazed by the events that occurred because unusual things often happen in their world. Alternatively, the events in Caractacus's story actually take place after the events of the movie. Baron von Bomburst had to have heard about the flying car from somewhere, right?

The Child Catcher is in some way related to Severus Snape.
Self-explanatory, really. The difficult part is that the Child Catcher having descendants would require him to have, you know, children. But hey, Snape's father was a Muggle and flouncing around in black robes with a big nose while being mean to children are genetic traits, right?

The Child Catcher is Willy Wonka's father.
At the time that Roald Dahl was brought in to work on the script for Chitty Chitty Bang Bang while having finished "Charlie and the Chocolate Factory" four years earlier, which (as Dahl chronicled in his short story 'Lucky Break') started out as a short note: "A chocolate factory - run by a lunatic". The original book of "Chitty" doesn't have the Child Catcher, and Dahl needed a proper henchvillain - so why not use the same lunatic twice, but make him even more vindictive the second time?

So: the Child Catcher, following the events of the film, expatriates himself to Britain, taking with him his wardrobe, cart and making a living as a sweet-maker under the name "Wonka", in the factories of Lord Scrumptious. After marrying a pretty-looking Englishwoman for citizenship, he fathers a child named Wilhelm, and inspires him in his choice of clothing, talent for sweet-making...and manic loathing of children. It is this loathing that causes Wilhelm - "little Willy" - to develop his unique personality - a secret hatred of himself caused by his father's violent upbringing.

When he realises he cannot seek revenge on the Potts family, as Caractacus is now the son-in-law of his boss, he satisfies himself in becoming the factory manager; at his deathbed, he tells "little Willy" to carry on his work. To this end, Willy Wonka becomes such a successful maker of sweets that he founds a rival company and buys Scrumptious' factory - and then begins his mission...building better and more fantastic sweets than ever before and ensnaring only the most wicked of children for punishment, in order to set the others an example! In his grave, the Child Catcher sleeps easily. His legacy is in good hands...