Deliberate mistake: There are no lights ever to be found in the underground world and the ceiling is literally the surface's ground, but there is still a perfect level of lighting regardless.
Deliberate mistake: I know this has been disregarded for the fun effect, but gasoline motors require air to work. When Edgar drives his tricycle into the river while being chased by Napoleon and Lafayette, it should have stalled and stopped working.
Deliberate mistake: When the family first entry Three Chimneys they have a single lamp as a light source. Entering from the door at the rear of the shot, everything in front of them should be in darkness to the viewer, but it's lit. Things in the background are lit even though there would be no line of sight to the light source. This is because lighting was added on set to allow the viewer to see things better, even though it ruined the realism.
Deliberate mistake: The German tanks in this movie are not really Tiger tanks. They are Russian T-34's made to look like Tigers. The T-34's are done up very realistically, including Zimmerit (the wavy pattern on the hull of the tiger), which was an anti-magnetic paste put on the tank.