(at around 46 mins) EVE is up and awake when the Captain pushes the green button that starts the tape of Shelby Forthright's briefing. But as WALL·E creeps away from the screen toward EVE, we glimpse EVE still strapped to the cart that brought her to the bridge.
(at around 22 mins) The waste cube that WALL·E produces during his introduction to EVE is gone in the following shots.
(at around 1h 19 mins) AUTO rolls the Axiom to the right by spinning to the right. After the Captain switches to manual, he levels the ship by also spinning the wheel to the right, not the left.
(at around 1h 15 mins) EVE's facial dirt markings disappear and re-appear. She gets several dirty markings on her otherwise pristine white exterior while in the garbage hold. A long dark stain runs down the right side (her left) of her "eye screen". When she flies WALL·E and M-O out of the garbage hold into the corridor, and is photographed aiming her weapon at the steward robot, and in shot when locking the steward away, the marking is clearly gone. Immediately after, as she is flying down the corridor, followed by a growing group of faulty robots, the mark reappears. During the battle with the large contingent of steward robots, in the beginning when she shoots a steward, the mark is gone, but as she shields herself when the 'massage' robot is let loose, the mark reappears.
(at around 7 mins) WALL·E records part of the the song "It Only Takes A Moment" from "Hello, Dolly!" and then plays it when he goes outside to look at the night sky. When he replays the song, it starts from an earlier point than when he hit the record button.
(at around 1h 19 mins) When the Axiom goes into a roll, the passengers and a considerable amount of heavy equipment are thrown off balance, rolling and piling up against one side of the common area. This should not happen as the gravity originates within the ship, not from an exterior source "beneath" it. Its artificial gravity should hold everyone and everything right side up no matter what position it assumes. It is possible that AUTO intentionally or inadvertently shifted the angle of the artificial gravity during the "roll" maneuver, but it was still presented as being directly caused by the roll, and there is no reason for such an effect to have been designed into the ship originally.
(at around 33 mins) While WALL·E is traveling in outer space, the stars in the background are blinking as they would appear on a starry night. In reality, the apparent blinking is due to the atmosphere between the star and the observer, so in space this phenomenon would not occur.
(at around 32 mins) The satellites over Earth appear to be standing still when the scout ship smashes through them (if they were moving at orbital speeds, such impact would have vaporized both them and the ship). However, standing satellites would fall down to Earth in a matter of minutes. But even if they were moving properly, such low orbits would've decayed in a matter of decades (let alone 700 years) due to atmospheric friction, solar wind, and interaction between satellites themselves. The only explanation is that all the satellites constantly support their positions with engines, but they appear to be defunct, and it's not likely that so many of them could still operate after 700 years.
(at around 34 mins) The first time we see the Axiom, it emerges from what appears to be a nebula. Although nebulae can appear as dense as shown from a very large distance (and after some heavy image processing), they are in fact much, much less dense than the Earth's atmosphere (otherwise they would quickly collapse under their own gravity), and utterly incapable of obscuring a ship as shown.
(at around 58 mins) When EVE and WALL·E try to reunite in space just after the shuttle pod self-destructs, twice WALL·E slows down when he stops pressing on the fire extinguisher (the two times when he's going very fast). This would not happen in empty space, where there is no gravity or friction to slow his momentum. WALL·E should continue in the same direction at the same speed when he stops pressing the extinguisher. Ceasing to press the extinguisher just stops him from accelerating faster.
(at around 8 mins) WALL·E's cockroach, Hal, sleeps in a "Kremie" (parody of the Hostess Twinkie). Twinkies grow stale and their cream filling evaporates after a few decades, yet Hal's interaction with it betrays it to be the same as a new Twinkie. This is most likely a joke implying that only cockroaches and Twinkies can survive the apocalypse.
(at around 47 mins) The original plan called for a mere five year trip, but the video instructions about the return to Earth show the same level of bone loss as the actual 700 year stay in space. Worse yet, such a short trip doesn't justify sending EVE probes at all, because, as we find out later, some people (including the president) have remained on Earth for these five years (the ship left in 2105 and the last message was sent in 2110). Evidently, the EVE program and the corresponding video were made in case the trip lasts indefinitely, possibly after it became clear that operation "Clean-up" is failing, but before it failed completely (or perhaps even afterward, but they forgot to cancel the previous order of not returning to Earth).
(at around 1h 19 mins) When the Captain raises the Holo-Detector, oxygen masks deploy over the humans' heads. However after the Axiom rolls to the right and the people slide out of their hoverchairs, the masks are gone. The masks can be seen retracting into the hoverchairs as their occupants slide out.
(at around 33 mins) In the film, WALL·E collides with Sputnik 1 (the first man-made satellite) during the liftoff of EVE's spacecraft. However, the real Sputnik 1 burned up in Earth's atmosphere in 1958, so WALL·E couldn't have possibly hit it. The filmmakers almost certainly knew this and included it anyway as an incidental visual joke.
(at around 43 mins) In captain's quarters there are only five pictures on the wall of the previous ship captains, even though the ship has been in space for 670 years before the current captain assumed the position, indicating that the previous captains had served for 135 years on average. This is not an error, however - the dates under the pictures confirm that these captains served between 120 and 140 years each. See also the trivia section. Evidently, even despite such an unhealthy lifestyle, the life span of humans in the future is much longer, which does make sense, considering the increasing trend in life span during the 20th century.
When Wall-E and Eve return to the Axiom after the escape pod scene, there is a robot welding a light to the exterior of the ship. It has sparks shining light onto its body from welding, but the visor around its eyes is completely unaffected by the light. This animation error was fixed in the Burn-E short.
(at around 35 mins) When the spacecraft carrying the EVE units docks inside the Axiom, among the robotic arms that attach to the ship is a two-conductor device resembling a heavy-duty power connector. Just after it connects to the ship, several small, black marks appear around it for one or two frames. They appear to be rendering errors.
(at around 1h 15 mins) When the Kiosk bot finds paint on the floor that the paint bot hiding in a storage closet left, it stops, and when it stops you hear the sound of tires screeching, yet the Kiosk bot hovers above the ground.
(at around 34 mins) When the shuttle approaches the Axiom, we hear sounds characteristic of jet engines (regardless of the fact there's no sound in space anyway), but the shuttle has rocket-style engines.
(at around 38 mins) Although it serves quickly to introduce the audience to life on the Axiom, ferrying EVE from the probe ship through the public plazas and lido deck to her examination would be seriously out of protocol, especially after testing positive for contamination. She instead would have been immediately maneuvered quietly through private conduits to her destination.
EVE's mission at the beginning of the movie is to seek out life on Earth, but her immediate instinct is to shoot at almost anything that moves, for example, at 17 minutes 32 seconds, 18 minutes 40 seconds, and 18 minutes 59 seconds.
The humans aboard the space cruise have been there for over 700 years and have gotten overweight and unable due to laziness and "bone loss". They are stuck in a hypnotic state of constantly absorbing media. However, somehow they are still reproducing.
BNL's president claims that people on board the Axiom are suffering from "bone loss" due to the effects of "microgravity". Numerous scenes establish that the (artificial) gravity on board is comparable to that on Earth, and certainly can't be called "microgravity", which is a near weightlessness. Also, no bone loss (let alone a "slight" one) can explain the change in physical appearance of humans shown in the movie, and "a few laps around a jogging track" wouldn't be enough to reverse such effects, not by a long shot. Of course, most of those mistakes, if not all, are probably intentional, to show the president's incompetence.
Although WALL·E is a wonderfully flexible and animated character, in truth, with his main body being essentially a hollow compactor, there's simply no room on him for all of the machinery necessary to function in the myriad ways he does.