Adaptational Villainy: Depp's portrayal of Wonka. While the original book character could be a bit of a Jerk Ass at times, here he's more of an apathetic and self-absorbed braggart. Luckily, he gets better by the end of the film.
Also, Augustus Gloop, to a mild degree. As the tour group heads towards the Chocolate Room, he asks Charlie if he wants some of his chocolate, only to immediately tell him that he should have brought his own. In the novel and 1971 film he doesn't really do anything until he starts drinking from the chocolate river.
Adaptation Expansion: The subplot about Willy Wonka's childhood and his relationship with his dentist father.
Anachronism Stew: Burton likes making his settings more symbolic than realistic. Therefore, to see Charlie Bucket's family living in near Charles Dickens-style poverty in one scene and Mike Teevee's videogames in the next is a tad jarring for some, despite the Buckets having their own TV. And Charlie's grandpa gives him a Peace dollar — an American, silver, 1920s/30s dollar.
Artistic License - Geography: Düsseldorf is portrayed as an Alpine wooden-house village, instead of the modern industrial capital of the Ruhr, which is far from any mountains.
Art Shift: Music shift to be more precise, as each of the Oompa-Loompas' songs has a different theme. Augustus's is based on Bollywood spectacle, as suggested by Deep Roy. Violet's song is derived from '70s funk. Veruca's has a very Beatles-esque feel to it. Mike's is a Hard Rock song.
Big Door: The Chocolate Room has an Inverted case of this — the door is incredibly tiny, likely so Oompa-Loompas can easily get in. (Mr. Wonka also claims it's "to keep the great big chocolate freshness inside!") The space is so small that the normal-sized protagonists are slouching.
Cloning Blues: Not the Oompa-Loompas, but rather the actor playing them.
Cultural Translation: Both Mike Teevee and Violet Beauregarde are American in this version (and Augustus Gloop is German) — although since the characters' nationalities were left deliberately ambiguous in the book and the tickets were explicitly said to be available all over the world, this is a relatively realistic touch. (It's also a bit of Lost in Imitation — it follows on from the 1971 film, which, unlike the novel, assigned nationalities to the brats.) On a less thought-out level, though, several of the English characters use Americanisms (like "candy" when referring to sweets), and their currency is, for some reason, dollars. For that matter, the opening scene implies that the factory may be in France, as the bicycles are motorized in a way that was only mass produced in France and not exported as a mass-market item.
Fantasy-Forbidding Father: Willy Wonka is given one of these as part of the Adaptation Expansion. Mr. Wonka, Sr., is a dentist who doesn't allow his son to eat candy, driving Willy to rebel against him to achieve his dream of being a chocolatier.
For Want of a Nail: Because of the increase of demand for chocolate due to the contest Mr. Bucket's job (toothpaste factory) makes extra money and decide to modernize, this results in Mr. Bucket losing his job. Later, he gets a better-paying job at the same factory repairing the machine that replaced him!
Foreshadowing: When everyone is entering the factory, Wonka seems to have trouble saying the word "Parents," which at first one might just assume is part of his eccentricity, however, it turns out to be a big plot point, what with his father issues and all.
Charlie asks how the Oompa-Loompas knew Augustus' name (and personality) in their Crowd Song, a Plot Hole that the book doesn't address with regards to any of the kids. Wonka claims it's skilled improvisation, but...
Mr. Salt remarks on how choreographed the Augustus number looks — implying that Wonka researched his victims, planned traps for them, and trained the Oompa-Loompas to celebrate their downfalls in a masterpiece of pre-planning.
When Wonka sizes up the kids for the first time, he remarks that Charlie's "just lucky to be here, aren't you?"
Lost in Imitation: While this film mostly avoids this trope with regards to the 1971 version, it does keep the same nationalities that film established for the children, while also giving most of them hometowns — Augustus is from Düsseldorf (which suffers from a bad case of Hollywood Geography), Veruca is from Buckinghamshire, Violet is from Atlanta, Mike is from Denver, and Charlie is still ambiguously British/American. Keep in mind that in the book all the characters' nationalities are ambiguous — most subsequent adaptations have picked up on the 1971 precedent.
Oompas: Veruca Salt, the little brute, has just gone down the garbage chute!
And she will meet, as she descends, a rather different set of friends!
Oompa: A fish head, for example, cut this morning from a halibut...
The Mel Brooks Number: Danny Elfman turns the Oompa-Loompa songs into a gorgeously orchestrated game of Genre Roulette, but the lyrics are still about naughty kids getting their comeuppance, and the visuals spoof everything from Busby Berkeley numbers to heavy metal videos.
The Monolith: Featured in a demonstration of Wonka's matter transmutation device...as part of a clip straight out of 2001: A Space Odyssey, no less.
No OSHA Compliance: Pretty straightforward. The overhead railings in the Inventing Room are particularly egregious. Amusingly, the one time the trope is subverted is in the Nut Room, with its so-inconvenient locked safety gate.
Not His Sled: Charlie is the last kid standing, but initially has to refuse the offer to become Mr. Wonka's heir because he won't let him bring his family with him. Only when he helps Mr. Wonka reconcile with his father is the happy ending free to commence.
The scene where Wonka sends the giant chocolate bar to the TV is one to 2001: A Space Odyssey. Complete with a monolith and "Also Sprach Zarathustra".
The following scene where Mike's dad rescues him from the TV set after he gets miniaturized himself: "Help me! Help me!"
Signature Style: Tim Burton likes to create a contrast between places of wonder, which are bright and colorful, and mundane places, which are dark and dreary. In the context of a Roald Dahl adaptation, it works.
Spared by the Adaptation: The toothpaste factory where Charlie's dad used to work. In the book, it was said he lost his job because the factory went bankrupt. In the film, the factory fired him and bought a machine to replace him.
Spoiled Brat: Pretty much all of the other kids, but Veruca — DEAR GOD — she takes this up to the prime maximum.
Technology Marches On: Mike used his computer to deduce the location of one of the Golden Tickets. In the 1971 film, a squad of professional programmers spend a lot of time and money to develop a massive supercomputer for this very purpose and suffer an odd A.I. Is a Crapshoot moment - see that page for details.
Technology Porn: The opening sequence showing the creation of the chocolate bars.
Up to Eleven: In Willy Wonka's flashback, Willy decides to run away from home after an argument with his dad. Wilbur responds, "I won't be here when you get back." Neither is the house.
Where The Hell Is Springfield?: Due to the book never being clear on whether Charlie Bucket and the Factory are located in England or America, Burton purposely made it ambiguous in the film; English and American accents are thrown around indiscriminately, people drive on the right in some scenes and the left in others, and paper money consists of bluish-pink "guinea" notes. And despite the entire population of the town (apparently) speaking English, the motorized bicycles used in the opening are uniquely French.