When Wall-E falls and damages his right "eye" he stumbles around as if blind even though his left eye is undamaged. However, with one eye he loses binocular vision which is needed to determine distance to objects, so stumbling and disorientation is to be expected.
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.
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.
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.
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.
When WALL·E first adds the Zippo lighter to his collection, he very carefully places it in the lighter bin facing out. When he first rotates the junk bin after he meets EVE, the lighter is gone. It returns again when EVE goes to pick it up.
EVE's facial dirt markings disappear and re-appear. EVE 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.
When WALL-E escapes the shuttle engines blasts, he's shown digging himself in directly beneath the ship, in a centered position surrounded by the three backblasts. When he comes out again, he bumps his head against one of the engine pods which is now directly above him, with the nozzle in very short distance.
After the vacuum robot sneezes on WALL-E, blowing off most of the makeup on his face, we see WALL-E's point of view as he looks at the other robots and for EVE. The next shot we see of WALL-E's face is after EVE goes into Diagnostics and it is clean of makeup. The vacuum bot didn't get a chance to clean WALL-E's face, yet the makeup is gone.
During the liftoff of the Axiom Return Vehicle with Wall-E clinging to the side, we look down and see that the rocket is rolling to the right. A medium shot from behind shows the rocket is rolling to the left. Then a wide shot from above shows the rocket finishing a roll to the right.
While WALL·E is traveling in outer space, the stars in the background are blinking as we would see them do 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.
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.
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 in outer space as the Axiom has no gravitational force acting on it, so its artificial micro-gravity should hold everyone and everything right side up no matter what position it assumes.
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.
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.
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.
When the Captain raises the Holo-Detector, oxygen masks deploy over the humans' heads. But 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.
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).
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.
Contemporary humans are computer generated cartoons but their ancestors, such as Buy N Large president Shelby Forthright and the actors in the Axiom ad, are all played by live actors. After hiring Fred Willard to play Forthright, the filmmakers made this an intentional stylistic choice to show that humans have greatly changed during 700 years in space.
WALL-E did not find his plant inside a closed refrigerator through which sunlight could not penetrate. Although it was behind a refrigerator door, the door had been removed from its hinges and was propped up against the corner of the fridge. WALL-E cut the door with his laser simply because it was too big for him to move as one piece.
The holographic billboards and advertising sound systems are powered by individual solar panels so they could still function without a working electric grid. Wall-E's truck also has solar panels and he uses a pile of (700 year old) car-type storage batteries at night. (However, the power source for the ship crane electromagnet is unexplained.)
In an exterior view of WALL-E's life pod during the ejection scene, the pod's headlights have cones of scattered light. Although these would not appear in a vacuum, it is clear that Axiom is not in a vacuum, but inside a very dense nebula (which is a goof on its own, though), and also probably surrounded by all the air ejected during the frequent garbage removals. Moreover, most of the light scattering effects, if not all, can be produced by the lens of the camera and the air inside it, and it is known that the filmmakers tried to simulate the effects of a real camera (see trivia).
Even if Wall-E's cutter is a laser (it could be a plasma torch for all we know), it's obviously very different (at least in appearance) from the ship's ranging laser used for landing, because it produces a visible ray and melts any solid it touches. So it's perfectly natural that WALL-E wouldn't recognize the laser ranging dot for what it is, because there is no visible ray (as expected from a real laser), or any damage to the ground.
Eve is shown as one of many bots to be sent to one of a multitude of possible life sustaining planets. When Eve returns to the axiom and presents the plant, the ship automatically assumes it is from Earth. If the ship was programmed to return to Earth upon receiving any origin of plant, sending multiple Eve bots would serve no purpose. However, in the scene when the captain analyzes the dirt WALL-E left on him, the computer says the dirt is from Earth, so the Holo-Detector most likely is able to also analyze the trace of the plant.
Wall-E produces his Zippo lighter out of thin air in the Axiom's garbage hold with Eve. He last had it on earth just before racing back to the rocket ship that returns to pick up Eve, but he may have stashed it in his garbage compressing compartment, as he does with many other items.
For the ship to have survived 700+ years in space, everything would have to be recycled (including the passengers). Dumping huge amounts of trash out in space would eventually deplete the ship of materials needed to maintain operations.
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.