Deliberate mistake: When Bender wins the poker tournament with five kings, Leo Wong holds up five fingers (on one hand). But all the characters in Futurama only have four fingers on each hand. (Confirmed on DVD commentary).
Deliberate mistake: When Aeon is fastening ropes to lower herself down into the security system, her hair parting has switched sides as she fastens the second rope, revealing a flipped shot. (00:08:25)
Deliberate mistake: When Baz is driving the 'movie car' the vehicle does not have hubcaps, but in the closeups of the tires there are hubcaps, and the tires change, plus there's tape covering the brand name at the center of the hubcap.
Deliberate mistake: At the speed trap, Tom points his radar gun at a turtle. From his perspective, he seems to be looking through some sort of scope with cross hairs and numbers on it at the turtle to line up the beam. However, when he then looks at the radar gun at the speed indicated as 1 MP/H, there is nothing on the gun where he could have been looking through such a scope. At best, the top of the run appears to have plastic iron sites. The scoped view would not have been from the device itself perspective since it would not need cross hairs or numbers on said cross hairs as that would be for a person looking through it to have reference points. This scope view of the turtle was most likely just added by the film makers to have a better visual representation of Tom aiming the radar gun at the turtle. (00:04:29)
Deliberate mistake: At one point during the big escape chase scene, Finnegan takes a turn and the jet-ski he and Trillian are on side-swipes a wall and it's clear that they're about to fall off. The film cuts away briefly and then we see them and they're zooming along again as though nothing happened. The scene is portrayed in real-time so there's no way they had time to spill, get back up again and build up enough speed in the time between edits. Slightly sloppy editing. (And this is not referring to the other moment in another mistake where the same thing happens when they exit the boat. It actually happens twice during the scene - that moment and this one).
Deliberate mistake: Montag's hair gets intermittently shorter, longer and shorter again (and acquires a "cow lick" that wasn't there before) near the end of the film. (Oskar Werner had clashed with Francois Truffaut and deliberately had his hair cut to spite director.)
Deliberate mistake: When they fight in the hangar and Troy is thrown back by the jet engine, his face and other parts of his body should have been burnt quite heavily. Such a jet engine has temperatures higher than 450°C about 5 meters away, and Troy is even closer than that.
Deliberate mistake: After the SAD unit shoots down the command module, Christopher falls to his knees in sadness. In the next shot, the mercenary supposed to be pointing his gun at his head is looking and pointing as if Christopher was still standing, as revealed when he actually gets back up again.
Deliberate mistake: The whole Monaco race sequence is totally (but deliberately) ludicrous. First no driver would be allowed without a fireproof mask and rest of required security measures, as Stark does. Second, the real-life security controls are very strict: When an accident occurs a safety car shows up, flags and audio advices signal the racing cars for them to lower their speed and avoid accidents. Nothing to do with the wild, uncontrolled race depicted here.
Deliberate mistake: When Robocain tries to use his chaingun on Robocop and it isn't armed, he snatches the remote unit from the OCP psychiatrist. If you look carefully, the remote unit changes from real to animated as soon as he grabs it.
Deliberate mistake: When Deckard wakes up in Wallace Corporation, there is a wide shot of the platform he is on. All four corners of the platform are empty in the wide shot. Deckard then looks at Wallace's visual aids as they float away, and then realises Wallace is standing in the corner directly facing where he is sitting, speaking to him. This corner was empty in the wide shot, with no sign of Wallace. Wallace could not have entered in between shots because Deckard would have seen him approaching or at the very least, heard his footsteps. This was likely done intentionally as to not give Wallace's reveal away too early. (02:08:55)
Deliberate mistake: When Metro Man flies towards the observatory to save Roxanne, we see a typical "the-characters-see-what-the-audience-sees" shot - a Super-Man-esque shot of him with his arms stretched out in front of him with his fists clenched. This shot is then projected onto a monitor that Minion is watching. It would be impossible to achieve this. It's as if there's some sort of camera on top of the observatory filming Metro Man, which there isn't. We see the observatory enough times to see that there isn't, and even if there was, the angle at which it would need to be at would be impossible to achieve. The shot of Metro Man on the monitor is positioned right in front of him, panning backwards. A camera would need to be very long to achieve this kind of shot, but there simply isn't one present.
Deliberate mistake: Empty magazines aren't that heavy, but when Alice kicks it into the face of one of the zombies, it looks like he's being hit with a baseball bat. (00:22:45)
Deliberate mistake: When Jared is picked up at the airport in the limo, after the scene where the limo is driving down the interstate it cuts to a shot of several tall buildings. In the street at the bottom of the shot, the traffic is moving backwards if you watch the facing of the vehicles. Looks as if the film plates were flipped. (00:06:30)
Deliberate mistake: During the train sequence at the end of the film in 1885, it is blatantly obvious that the train is not going the speed that the DeLorean's speedometer is showing. In some shots, the train looks as though it is going little more than 20mph. (01:38:55)
Deliberate mistake: The suit, rather than using many large cameras, should be created with many imperceptibly small cameras in between monitors. We need monitors to see what is on the other side of the suit, not camera lenses.
Suggested correction: The monitors are on the inside, behind the cameras.
Deliberate mistake: When Johnny Five is assembling the first toy robot, he takes a screwdriver to the neck and body of the robot toy, even though there are quite obviously no screws there for him to tighten.
Deliberate mistake: When Max opens the dog food, the lid should be all jagged because of the type of can opener he uses, but when dog and the gyro captain have the can the lid is cut smoothly. This was done so dog didn't get cut whilst eating out of the can.
Deliberate mistake: When Dave is in the pod arguing with Hal to let him back in, various patterns of light are projected on Dave's face presumably from the video screens that say NAV and COM and such. Light on such a screen would diffuse and not project like this. It is likely those screens had rear projection and they merely removed the screens for this effect.
Deliberate mistake: The energy the meteor would displace upon impact would have created a crater of significant size compared to what was portrayed. It also didn't appear to have any impact to the structure of the cavern it crashed into either.