Deliberate mistake: When Commander Taggert and Lt. Madison are about to press the blue button to stop the ship exploding, Lt. Madison's tunic is mostly zipped up. A few seconds later it is suddenly mostly unzipped. Those of you who have access to the DVD of the film can see that there was a deleted scene which was originally intended to go in here where she unzips her tunic to distract the aliens.
Deliberate mistake: The atmosphere on Mars is only 1% as dense of that as Earth, so 175kph windstorms would feel like a light breeze. They would have very little effect on the astronauts or MAV. The writers of the book and the film were aware of this, it was a small cheat to let the rest of the story unfold.
Deliberate mistake: Blofeld doesn't recognize James Bond in this film, even though they met face-to-face in the previous movie, "You Only Live Twice." There is a production-related reason for this. Ian Fleming wrote "On Her Majesty's Secret Service" in 1963 (in which Bond and Blofeld met for the first time), and he wrote "You Only Live Twice" in 1964. However, "You Only Live Twice" was adapted for film first (in 1967), and "On Her Majesty's Secret Service" was adapted afterward (in 1969). Because the 1969 film was so faithful to its source material, Blofeld and Bond are basically meeting for the first time...again. The producers were aware of this continuity problem and intended to have James Bond undergo plastic surgery for "On Her Majesty's Secret Service" (which would conveniently explain Blofeld not recognizing him, as well as the fact that Sean Connery had been replaced by George Lazenby in the lead role). But the plastic surgery idea was discarded in faithfulness to the novel, resulting in a glaring continuity problem between the 1967 and 1969 films.
Deliberate mistake: At the end of the movie when everyone is on the bridge, the one female cop roundhouses the bad guy, who is clearly a white male in his 50's, but his stunt double is an Asian man (with different colored hair). They use the same stunt man a few other times for people he doesn't even look like.
Deliberate mistake: Not only is the angle of the moonlight that shines through Jack's prison cell window intentionally exaggerated to enhance the shots with Jack, doggy, Koehler and Twigg, but in relevant shots, the moonlight is not seen coming through the window or the broken wall. Nor is it reflected on the floor outside the cells or in the cell next to Jack, particularly in the shots from the dog's POV looking up the corridor towards Jack. (00:36:00)
Deliberate mistake: During the moon buggy chase scene in the desert one of the Ford LTDs crashes and the front fenders,inner fenders, and doors fall off. Even if the car fell off of a cliff this couldn't happen unless all the bolts were moved previously.
Deliberate mistake: When Norman picks up Marion's supposedly naked body to carry it to his trunk, a bra is visible through the shower curtain. Gus Van Sant included this goof in his 1998 remake.
Deliberate mistake: When Eddie and "Jennifer" are walking around the house alone, she is trying to tell Eddie that she's really Sara. But by the time she is explaining that, Eddie has disappeared. She doesn't find him until later. But from the moment she finds him (and he is talking to her) he calls her Sara, despite never actually hearing her say that. Also, after they all get back together, a few of the other people start calling her Sara as well, but no one actually heard that either.
Deliberate mistake: In the scene in which Ace is in the asylum, he breaks into a storage closet to view Finkle's belongings that were left behind when he escaped. At first the doorframe is such that the door closes against about an inch of wood, meaning the lock would be behind this wood, so Ace couldn't pry it open. In the closeup, the door's flush against the frame so Ace can use the sign to get between the door and the frame. In the wide shot it's back to how it was. (00:58:55)
Deliberate mistake: Almost trivia, but not quite. When Mystique's looking through the guard files to find a suitable candidate, lots of photos flash up very quickly before she finds the guy she uses. Of note is that Bryan Singer pops up in guard uniform (with his own name), and so does someone called "Donner, L". This is most likely referring to Lauren Shuler Donner, one of the producers, and sex is specified as "F", but the photo is of a stubble-coated man. (00:23:10)
Deliberate mistake: During the finale, the backround looks like a sunset and there is a big door in the back. Watch closely and all of a sudden from one camera angle to the next (it's right after the big puff of smoke), the background changes to an elaborate background of layers of hearts, the door is gone, and there are about 60 more extras onstage. During the DVD Baz explains that they filmed the scene with both backgrounds and it just so happened that the beginning was better with one and the end was better with the other, so they put the puff of smoke in there to distract the audience so that they wouldn't see the change.
Deliberate mistake: During the mob scene outside Saito's love nest, the same black Saab is seen getting firebombed twice. It was shot from two different angles, with the two shots played about a minute apart to give the impression of two cars getting bombed. Also, in the first angle it is clear the car has no engine.
Deliberate mistake: When the Alien appears behind Brett, we first see its tail lowering before the rest of its body, even though the tail is presumably how the creature was being suspended in the air. Immediately after chomping Brett's head, he and the creature are lifted upwards, again presumably by its tail, though it's not long enough to carry them the implied distance and it's unclear what it has latched onto in the first place. This scene starts a tradition of sorts, as both 'Aliens' and 'Alien 3' feature their own scenes in which an Alien grabs a victim and both are subsequently lifted upwards by a great height, presumably by the creature's tail, and the mechanics by which this is possible and even where exactly they're going off to are always obscured to the point where the creature may as well be wearing a jet pack.
Deliberate mistake: During the "breaking up" scene with Jim and Michelle when they're inside the cabin, her hair is crimpy, but when she walks outside and gets into her car, her hair is straight. This is because Alyson Hannigan filmed this particular scene during a break in the filming of a "Buffy the Vampire Slayer" episode. (01:15:40)
Deliberate mistake: In the Extended Edition, the location of the Tomb of the Stewards is shown to be behind the city of Minis Tirith, at the cemetery on the mountainside, accessible via a long bridge. Flaming Denethor later runs to the far prow of the city, leaps off and plummets. The distance between the two areas makes it is obviously entirely impossible for someone, even adrenaline charged Denethor, to run this distance while his oiled flesh burns. Admitted on the commentary that it's poetic license, due to director Peter Jackson's long awaited vision for this dramatic shot. (00:13:15 - 00:30:50)
Deliberate mistake: The same scene of William Bendix at bat swinging and missing is used repeatedly in the film.