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)
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.
Continuity mistake: When Wall-E's caterpillar track is disintegrating, leading to a bumpy ride, it's his right-hand side track that is shown broken. When he checks it against another Wall-E unit, he picks up his left track, which is now broken. Finally, when repaired, the camera shows his right track again running smoothly. Wall-E hasn't turned round either - his 'lunchbox' is still on the back in all scenes. (00:04:35)