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.
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 Polly reaches for her camera on the tree log, Joe grabs her right hand and the camera is in her left. In the next shot, he's holding her left hand and the camera is in her right hand.
During the robot 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.
In the aircraft hangar base, a plane can be seen to be shot down and blocking the exit to the hangar. However, moments later Joe can be seen exiting the hangar where this plane was gunned down, but when he flies away the stricken plane is nowhere to be seen.
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 the rocket boost phase, Joe and Polly should be subject to several Gs of acceleration, but they continue to move (and objects continue to fall) normally.
Laurence Olivier is listed in the end credits as 'Sir Laurence Olivier'. Although knighted in 1947 and becoming Sir Laurence, he was made a life peer in 1970, becoming Lord Olivier. When one becomes a peer, the title 'Sir' is discontinued and, thus, incorrect.
When the rocket door open at 90,000 meters -- an altitude of about 56 miles -- Joe and Polly should have been almost instantly asphyxiated.
When Joe and Franky 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.
After the P-40 surfaces on Totenkopf's island, Polly sees the plane's registration "h11od" reflected in the water and one of the dashes is has moved, it reads "polly". In order to make the gag obvious, the filmmaker flipped the reflection horizontally.
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.
On two occasions, Franky gives the order "All hands on deck" when she means "battle stations" or "general quarters." As this film is set in an "alternative" reality, matters such as command protocol are not bound to history.
In the underwater scene where Joe's "submarine plane" is forced backwards, it makes a sound like an airplane flying through the air. As the entire film is a fantasy and inspired by hokey 1930s serials, this is to be expected.
At one point in the film, Polly takes a flash picture, but her camera contains no flash attachment.
In Nepal, none of the actors' breath is visible, despite the apparently freezing conditions.
When Dex first tests his ray gun, the reflection of the beams in his goggles travel in the wrong direction.
When Frankie ejects from her plane underwater, no rush of air bubbles escape the cockpit.
When the destroyed robot is delivered to the Sky Captain's base, we can see that CGI trucks carrying the robot have no drivers.
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 Schröder (in office 1998-2005).
Joe is carrying Dex's ray gun while he is locked in the dynamite shed, but he doesn't use it to get out.
The Mystery Woman is unconscious as the rocket takes off, yet somehow she is aboard the rocket in flight.
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.
While underwater, Joe exclaims, "My rudder's jammed." In fact, it is his elevator that is jammed.
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.
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.
Joe refers to "ancient" sailors navigating by the stars. So did WWII pilots like Joe, and plenty of navigators since.
The German rocket's display showing its height contains three spelling
mistakes: "VERSTARKER" (booster, amplifier) should be written with A-umlaut ( VERSTÄRKER ) 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".