Sky Captain and the World of Tomorrow is a 2004 movie homage to the Two-Fisted Tales of the 1930's. The film follows the adventures of Ace Pilot 'Joe' Sullivan, known as Sky Captain (Jude Law) and Intrepid ReporterPolly Perkins (Gwyneth Paltrow).They begin investigating the affairs of the mysterious German scientist, Dr. Totenkopf, after his machines attack New York City, searching for something. Further implicating Totenkopf is a string of kidnapped scientists, all of whom point back to Totenkopf's work...The plot shamelessly uses the outrageous gadgets and cliches of the Pulp Magazine and Comic Book genres, plus numerous shout outs to other media of the period. Filmed with live actors against computer-generated surroundings, the movie did not make enough money to offset its production costs, so a sequel is unlikely.
Zeppelins from Another World: The Hindenburg III docks at the Empire State Building in the opening scene, though in reality the docking spire was inoperable from the beginning due to strong updrafts and the lack of a mooring point for the other end of an airship.
Other tropes include:
Absurdly Dedicated Worker: Dr. Totenkopf's machines carry on his work of assembling a "Noah's Ark"-type rocket and loading animals on it despite him having died 20 years prior.
Action Dress Rip: Polly tears her skirt to run better during the NYC robot attack. But leaves on the heels....
Aerial Canyon Chase: The title character flies his fighter plane along the streets of New York just above ground level while trying to escape Dr. Totenkopf's robot ornithopters.
Alternate History: There is a Hindenburg III zeppelin in the opening scene, which implies either that the first Hindenburg did not explode, or else its explosion was not an impediment to further airship construction.
Anguished Declaration of Love: Spoofed. Joe Sullivan believes Polly Perkins deliberately sabotaged his plane in China while Going for the Big Scoop. When they're trapped in a cave packed with dynamite that's about to explode, Joe looks her in the eyes and asks...if she really did cut his fuel line. Polly is understandably annoyed that they're going to spend their last moments on Earth discussing this point. And on Totenkopf's island, she admits she did. A pissed off Joe then admits that he did sleep with Franky.
Apologetic Attacker - Played With: The note Totenkopf leaves at his death chair reads "Forgive me", and there's indications he tried to shut down his entire project, and it's implied his robot assassin/kidnapper rebelled when he tried to shut everything down.
Joe: Could we just for once die without all this bickering?
Bedmate Reveal: After an Outrun the Fireball moment, Polly wakes up naked in a bed next to an equally naked Joe. An embarrassed Polly tells him to turn around, which a grinning Joe does only to find he's also in bed with their guide, Kaji, who is also naked.
Billing Displacement: A sterling example. Law and Paltrow are billed diagonally. On the same card, Jolie gets the "and" honor by being billed as "and Angelina Jolie". They thus manage a triple simultaneous diagonal bill where everyone gets a position of honor.
Camera Obscurer: Polly Perkins spends much of the movie with only one frame left on her only roll of film, and wants to save it for a truly awesome photo. In the film's denouement, she decides to take a photo of Joe Sullivan, only for him to look at her and say "Lenscap".
The two metal tubes that Polly Perkins received from Dr. Jennings.
Dex also built Chekhov's Ray Gun and is seen chewing Chekhov's Gum.
Chroma Key: The actors used only the most basic sets and props, with CGI backgrounds used in every shot. This was allegedly done for two reasons: One, the producers wanted to give the movie a "comic book" atmosphere, and two, the studio was too small to accommodate such large sets.
Cut and Paste Environments - Toward the beginning of the movie, just after the robots attack Manhattan, Sky Captain lands at his base and drives his plane into a huge hangar. At the top of the doors of the hangar are these huge windows of 8x10 panes. In every window, some of the panes are broken. In every window, it's EXACTLY THE SAME PANES that are broken.
To a lesser extent, the superelectric field outside of Totenkopf's room that disintegrates anyone who steps on it, first stripping them to a skeleton, then pulverizing that to dust. An unfortunate no-name scientist finds this out the hard way.
Doing It for the Art: The film's creator spent years developing software to achieve a film with this specific look, and then pitched a film around it.
Fake Brit/Fake American: Englishman Jude Law plays the American hero, while American Angelina Jolie plays "Franky". Jolie's accent was mocked by some critics, though she's merely riffing on the stiff-upper-lip jargon of British war propaganda.
Giant Flyer: The protagonists encounter giant prehistoric birds on Totenkopf's island.
A God Am I: Totenkopf, in the video that plays while his rocket is rising through the atmosphere. It plays a twisted version of the first few verses of Genesis, replacing him as God and him seeing that "Man was evil."
A particularly noticeable example is a button labeled with "Dringlichkeitsfreigabe", which then gets translated as "Emergency Release", while it actually means "Urgency Release". It should be "Notfallfreigabe/-abkopplung/-entriegelung/-freisetzung".
The German newspaper headline about the robot invasion translates to "Very Big Metallc [sic!] Machines Steal Steal Reserves"
The Grotesque: The sole survivor of Dr. Totenkopf's uranium mining and experiments.
Gunship Rescue. An entire fleet of heliocarriers turns up to rescue the protagonists at the end, though they don't really need saving by that stage. And Dex has a Big Damn Heroes moment when he arrives in a hoversled just in time to save Joe and Polly from the swarm of flying killer robots.
Herr Doctor: All the scientists are German and Austrian.
Homages: The attack by giant bipedal robots is copied from the 1941 Superman cartoon "The Mechanical Monsters". Their laser sound-effects are the same as the Martian Disintegrator Ray in the 1953 The War of the Worlds film; similarly Polly's phoned-in report on the attack uses lines lifted from the famous Orson Welles radio broadcast. On seeing one of the robots, Dex mutters "Shazam!" The silhouette of Godzilla can be seen in a newspaper from Japan. During an underwater sequence we see both the wreck of the Titanic and the ship from King Kong, complete with ape-holding cage. King Kong himself can be seen at the top of the Empire State Building during one shot with the robots in the streets. The flying robots on Totenkopf's island have the same chest controls as Commando Cody's Jet Pack. The Wizard of Oz is seen playing in the cinema where Polly meets with one of the scientists, and the entire Totenkopf hologram head sequence is a massive homage to the The Wizard of Oz's giant head scene (Captain Sky even mentions the film when the Hologram appears and starts speaking.). Et cetera.
(Sky Captain and Polly step across the booby-trapped threshold, holding hands, in lock-step and are relieved to be unharmed)
Dex: "...I meant throw something."
Justified Title: The Character Name and the Noun Phrase title is obviously a reference to the retro-futuristic nature of the movie, but "Sky Captain" is the nickname of the main character, and the villain calls his scheme to seed life on another planet the "World of Tomorrow".
Lois Lane: While she doesn't have the myopic identity problems Lois had, she's definitely filling this role in the film as the no-nonsense female reporter determined to follow the hero to the end and get the story.
Mad Scientist Laboratory: The laboratory of Dr. Walter Jennings (with mutated fetus and tiny elephant), and the room in Shangri-La (shown in a deleted scene) where Totenkopf conducted experiments on radiation victims from his uranium mine.
Meaningful Name: "Totenkopf" is German for "death's head." (Totenkopf wanted to destroy the world and create a new one out in space.) It also harkens back to Nazi Germany's SS "totenkopf" division that was in charge of the concentration camps.
My God, What Have I Done?: Totenkopf, realizing the error of his ways and unable to stop what he started (the rockets he's sending off the planet will destroy the Earth's atmosphere to escape its gravity), simply leaves a note on his corpse: "I'm sorry."
Never Trust a Trailer: Angelina Jolie is in the movie for all of 15 minutes, but you'd think she was a main character.
No OSHA Compliance: The walkways inside the rocket ship. They're barely wide enough to walk on, and have no railings. Justified in that the "actual" Dr. Totenkopf is long dead, and his operation is being carried out automatically via robots, drones, and mechs. Obviously they would not bother with human safety hazards.
Joe and Franky: PROTECT THE RABBITS!!! PROTECT THE RABBITS!!!
One Bullet Left: Polly is down to one shot left in her camera, so she's forced to forgo the chance to photograph the lost kingdom of Shangri-La, a top-secret flying aircraft carrier, a giant prehistoric bird, and every creature on Earth being loaded two-by-two into a giant rocketship. In the end Polly passes up the Scoop of the Century for a photograph of Joe... who promptly informs her she left the lens cap on. note Except the point of view during the shot is facing Polly and the front of her camera, and the audience can clearly see the lens cap is not on. Though you could handwave this as Joe messing with her again.
Percussive Prevention: Joe knocks out Polly to stop her from accompanying him on a one-way trip to destroy Totenkopf's rocketship. It doesn't work.
Godzilla appears on one of the newspaper headlines in a "blink and you'll miss it" cameo
In the scene where Sky Captain is flying back and forth down the street attacking the giant robots, in one shot the Empire State Building is framed in the background... with King Kong hanging from the top.
Big slow-moving robots that are Immune to Bullets and fly around casting ominous shadows and stealing things from baffled citizens? Seems to pay homage to this old Superman cartoon. 
The sound effects of the giant robots' lasers are the sounds of the Martian heat rays in The War of the Worlds.
Sidekick: Dex, to Joe (Sky Captain). But there's a lot more to Dex then this, he may look like a skinny little nerd but he's taken a level in badass and has matters well in hand when Joe finally arrives to 'rescue' him. To his credit Joe doesn't seem very surprised and just asks for a heads up on the plan.
Sitting Duck: The Flying Legion is caught on the ground by an air raid launched by Totenkopf's robot flyers.
That Was the Last Entry: When the group finally gets to Totenkopf's office, they find his papers and discover that "the last entry in his journal was made on October 11, 1918", 20 years before the setting of the film. Shortly thereafter, they find his mummified body.
Why Won't You Die?: Invoked word-for-word when The Dragon, beaten, revealed as a Robot Girl, and left for dead at the villain's island, sneaks into the rocketship to attack Joe one last time.
Would Hit a Girl: In a rare heroic/noble example, Joe knocks Polly out to keep her from needlessly putting her life in danger.
Wronski Feint: Subverted. It looks like Joe is doing this with the ornithopters chasing him out over the water, when actually he has every intention of actually crashing into the ocean. His plane is able to transform into a submersible mode!