One of the German newspapers shows a story placed in a nowadays edition of Frankfurter Allgemeine Zeitung (clearly recognizable by its unique typeface and the letters "FAZ" at the beginning of a story). Some of the FAZ stories deal with German financial/social politics during the government of Gerhard Schroeder (in office 1998-2005).
When on his P-40 plane, Joe and Polly are not wearing headsets. Wind on the fuselage, vibration and engine noise would make it impossible to talk to control tower and they'd have to scream to be heard inside the plane. Yet they speak normally, as if they were sitting in their living room.
In the scene where Joe and Frankie are talking to each other by radio from their "submarine planes," a buzz indicates that its a one way transmission and that they can only speak to each other one at a time. However, a moment later they both say "Protect the rabbits" at the same time.
The German rocket's display showing its height contains three spelling
mistakes: "VERSTARKER" (booster, amplifier) should be written with A-umlaut and the plural of kilometer is simply kilometer, without s at the end, and since nouns are capitalized in German it should actually read "Kilometer".
Joe constantly wears goggles while piloting his plane. In fact pilots of the era were trained to lower their goggles when going into combat to preclude glass or perspex slivers from bullet hits on their canopies from getting into their eyes.
The first newspaper shown reports the Hindenburg III docking at the Empire State Building on October 6th, 1939. But in shots of the newspapers shown during the montage after the first attack by the robots, you can clearly see the date of publication was March 15th, 1939. And later, Polly says that the current date is March 2nd.
When Sky Captain and Polly are running across the log bridge, he fires a 1911-style semiautomatic pistol at one of the birds. When he falls and drops the gun, it's the revolver he used against the robots earlier in the film.
During the Giant Robots scene you can see King Kong climbing the Empire State Building in the background. This doesn't make sense because later in the film you see the Venture ship from the King Kong movie heading toward Skull island during the submersible plane scene. The ship even has a empty giant cage on board.
On board the Hindenburg III, Doctor Vargas asks the boy (in German) "Könnten Sie mir bitte versichern, dass dieses Paket überreicht wird". The subtitles translate this as "This parcel must be delivered the moment we reach port". In fact, the correct translation of the German is "Could you please assure me that this parcel will be delivered".
During air battle Sky Captain's plane had been shot and his fuel tanks in its' wings are damaged and leaking fuel. After going under water and coming out again there is no damage and they loose fuel no more.
Several problems with the camera Polly is using, the Argus C3. (Produced from 1939 to 1966, there are thousands still in use, including one this author has had for 50 years.)
1. It was released in October 1939, yet Polly was in possession of it when Wizard of Oz was released in August of that year.
2. She is shown taking flash pictures with it, with no flash unit attached. (She would have to take the camera out of its carry case to attach the gun-grip flash.)
3. If not meant as a joke, you can't take a picture with one "with the lens cap on" as it didn't have one - the full case (which they had severely modified for the movie) has the "lens cap" built in to its cover.
4. She is shown taking picture after picture without winding.
5. She is never shown "cocking" the shutter, which is powered by a spring release mechanism.
6. The metal "frame counter" may be from the older model C2, but the C2 was incapable of using a flash unit at all.
7. The digital frame counter shown (when Polly complained she only had two shots left) never existed - only the frame counter wheel (which does correctly shows only two shots remaining.)
When Joe's plane runs out of fuel, the first thing he does is lower the landing gear, which is literally the last thing he would do, as it would greatly reduce his glide ratio. Even an inexperience pilot (let alone a "Sky Captain") in that situation would wait until the last moment to lower the gear.
The motion of the ornithopters is wrong. As the wings flap, the fuselage stays in one place. Physics says it should bob in the other direction (watch a bird fly: as the wings go up, the body goes down).
Laurence Olivier is listed in the end credits as 'Sir Laurence Olivier'. Although knighted in 1947 and becoming Sir Laurence, he was, however, made a life peer in 1970, becoming Lord Olivier. When one becomes a peer the title 'Sir' is discontinued and thus incorrect.
During robots scene in the beginning Polly dropped the camera and it rolled and fell through the sewer shaft. She tries to reach it and as she touch it it rolls out of her reach. The straps are even further from her reach, but in the next scene she reaches the camera by the strap.
The movie is plainly set in an "alternative" reality, so apparent errors of history and geography can be discounted. We don't know how many World Wars there have been in their reality, nor when films, etc, were released.
When Joe's plane dives into the sea and converts into a submarine, the force of impact with the water would have surely sheered the wings off of a normal P-40. However, as the plane is obviously been made watertight, as well as fitted with sonar, precautions must have also been made to brace the wings from impact.
Joe and Polly land dead-stick (without fuel) on the carrier and the carrier is attacked only a few moments later. They take off again while the attack is still ongoing, but the the plane is now apparently fully fueled.
After the P-40 surfaces on Totenkopf's island, Polly sees the plane's registration "h-11-od" reflected in the water and one of the dashes is has moved, it reads "po-l-ly". Also a reflection flips the image upside down (like "y-ll-oq"), it does not rotate it 180 degrees.
Headlines in German newspaper shown after the attack of the robots is full of errors. Main headline is "Sehr Große Metallc Maschinen Stehlen Stehlen Reserven" which translates to "Very Big Metallk Machines Steal Steal Reserves". Another headline says "Schlechte Desends Nach Landschaft" which means "Bad ??? On Landscape" (the word "Desends" means nothing in German). Furthermore, only the first word and nouns are capitalized in German headlines. This line was probably to mean "Evil Descends to the Land" in which case it should appear as "Das Übel kommt über das Land". The same goes for Russian newspaper that is titled "Voice People's" and shows headline full of semantical and grammatical errors ("Gigantic Metallic Nation's Reserves Steals Machines Coal, Oil and Uranium. National Leader Attempt To Protect Reserves").
The goof items below may give away important plot points.
Incorrectly regarded as goofs
At the end of the movie, when Polly lifts her camera to take a
picture of Joe, the lens cap is NOT on the camera, even though Joe states that it is after she snaps the picture. This the final poke at Polly from the Captain.
Towards the end of the movie, under normal circumstances the g-forces from the rocket's high speed would cause it to be almost impossible to move as easily as Joe and Polly do. However, Totenkopf has invented anti-gravity devices, as is evidenced by the robots in the beginning of the movie. Therefore he may have created the rocket with some form of g-force protection to protect the animals inside.