Factual error: At the very end, Polly Perkins takes a spectacular picture, using the very last shot on her only roll of film. When Sky Captain tells her she left the lens cap on, she is mortified. But she would certainly know that on her Argus 35mm camera, all she had to do was remove the lens cap and retake the shot. Unlike modern idiot-proof cameras, hers has no mechanism to prevent double-exposures.
Factual error: After the robots first attack New York City, a series of newspapers is shown. The German one is full of mistakes. It says "Sehr grosse metallic Maschinen stehlen stehlen Reserven." The word 'metallic' would be 'metallisch' in German and they would write robots as 'roboter'. 'Stehlen' (steal) is written twice.
Factual error: When Polly Perkins goes to Sky Captain's headquarters, she promises not to take any pictures without his permission, then proceeds to take a picture, holding her camera behind her. Before you can take a picture with an Argus 35mm camera, which is what she has, you first need to flip down a lever on the front of the camera that "cocks" the shutter. When you trip the shutter, the lever flips back up. But when Polly takes the picture, you hear the shutter "click", but the lever doesn't flip up.