Factual error: As a trash compactor Wall-E does not function logically. When he fills his chest compartment with garbage and runs his internal compactor, the cube that exits his body is the same volume as the trash he puts in, despite that trash having been compacted. He does not add extra trash to fill the empty space after running the compactor - there are three scenes that show him filling up only once with loose garbage and then ejecting a densely compacted cube. (00:02:30)
Suggested correction: You haven't noticed the exact shape of his body. The back sticks out a tad. Garbage fills the space and the back pushes in to compress it.
Continuity mistake: After the escape pod scene (but before the 'dance'), Wall-E uses a fire extinguisher to fly back and forth. Between every camera shot except one, all the extinguisher particles disappear instantly. (00:56:50)
Continuity mistake: When Eve fires a shot at the tanker they show an overhead view of the scene - there are three other tankers sitting on the starboard side of the exploded tanker. When the tankers fall like dominoes there are now four of them next to the exploded tanker.
Suggested correction: There is correct number of ships, but more likely wrong ship is burning in second image.
Continuity mistake: When Eve repairs Wall-E, you can see some tread segments are popped out, but when Wall-E powers back up they're all good as new. She doesn't replace his treads, just some gears.
Suggested correction: However, even if the treads are not changed, the wheels inside the treads are, which could well straighten up his treads.
Character mistake: Captain McCrea tells the passengers that it's the 700th anniversary of the Axiom's first flight. The Axiom has been in flight for 255,642 days. Actually, 700 years is 255,675 days. That figure includes the additional day in 175 leap years.
Suggested correction: Leap years only occur because of the earth's rotation around the sun. As the AXIOM is in space, there is no need to correct for the earth's rotation.
First, rotation is the spin of the Earth (which cause day and night). Revolution is the earth orbiting the sun (which causes years). However, this correction is not valid on the premise you're trying to present. Many films set in space still use Earth time, so a day is 24-hours, even though they're in space and there is no sunrise and sunset (although it's stated the Axiom operates on a 25-hour day). So they would use Earth's year, which takes 365.256 days. Since the Axiom isn't orbiting the Sun, it wouldn't experience a year, so they're using something else. The fact that they're slightly off suggests it's a writing mistake and there's no evidence they use an arbitrary 365.203 day year.
Continuity mistake: When picked up from Earth, Eve is placed into the first of five spaces (left). When unloaded on Axiom, it's the fifth on the right. (00:32:59 - 00:36:29)
Suggested correction: They spun around when they got off.
I thought this mistake was already corrected and I'm not sure why it was taken down. It does seem that we see the other side of the wall after the first shot. The robots spin around and are now facing the other way. They are still in the same order though.
