I can't really understand anyone seeing a film with a title like "Sky Captain and the World of Tomorrow" and complaining it didn't have enough depth. After all, it isn't as though the old Flash Gordon serials, or whatever else inspired this, had deep philosophical discussions and incredibly subtle characters.
Considering the ponderous and detailed effort that went into this film (the actors worked with blue screens, and almost literally everything else is special effects) it's amazing that it's also light on its feet enough to include humour and not take itself too seriously. Even the main villain is generated from images of Sir Laurence Olivier (dead since 1989, raising mildly troubling ethical questions). And it all done on a lower budget than you'd expect, though if the film has one major flaw it's probably a bit too much going on, so that eye has too much to take in. Just because you can animate three hundred enemy ships doesn't actually mean you should. Jude Law and Gywneth Paltrow are well cast because they look as though they could belong to the late thirties when the film appears to be set.
Roger Ebert talks about the "gee-whiz vigor" old serial adventures had, a "naive faith in science and pluck," and that's certainly to be found in Sky Captain. Sure, it's a little incongruous to see 1938 fighter planes going up against giant robots. And in a film where the characters say the "First World War" when the second one hasn't happened yet (they'd be saying the "Great War" probably) it's far too easy to get into nitpicking and miss the point. And the point, by the way, is the sheer fun of it. I fell for this film the moment I realised the giant robot beams had the same sound effect that was used in the 1953 War of the Worlds.