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Service" (which would conveniently explain Blofeld not recognizing him, as well as the fact that Sean Connery had been replaced by George Lazenby in the lead role).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: 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: 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: When Peter and Miraz are fighting, Peter stabs Miraz and then brings the sword back up for the killing stroke. There is no blood on the sword. This is deliberate on the part of Disney, so as not to show blood, but a mistake nonetheless.
Deliberate mistake: Bosley is a school crossing guard trying to help the Angels. The children behind them say they are gonna be late for school. Of course they're going to be late because there is not a school within 10 miles of where they are standing. There's trees and what looks like a huge mountainside on the other side of the street. You can see this more visibly as the car that is about to run over Bosley is approaching. Done for a gag, but still ridiculous. (01:09:05)
Deliberate mistake: After the Tusken Raider has attacked Luke, he raises his stick over his head and shouts. The movement of his clothing is extremely unnatural. During the editing, they put the same footage forward, then backward many times, to add emphasis to his movements, but it looks decidedly odd. (00:29:02)
Deliberate mistake: At the elephant graveyard, little Simba claws Shenzi in the face. When Mufasa saves Simba from the hyenas, the cuts are gone, a few seconds later. [This was done intentionally, I'm sure, for two reasons. The first being, Disney doesn't let fresh scars linger on the screen too long. Secondly, during that same scene when Mufasa rescues Simba & Nala, he claws Banzai in the rear. To stress the point later in the movie, that severe scar is shown too, but only briefly, it too disappears because of reason 1. Still a "mistake", but there's why.] (00:21:50)
Deliberate mistake: After Peter says, "We can't both have her lady," he shuts the window from the outside and the bottom pane is placed on the outside of the top stained glass pane. This is obviously done specifically for this shot so Peter would be able to shut the window and try to keep the Darlings from opening it. However, in the next shot as the Darlings succeed in opening the 'stuck' window, the bottom pane is on the inside of the top stained glass pane. (00:02:05 - 00:58:45)
Deliberate mistake: Towards the end of the movie fish are seen to swim down in order to submerge the net in which they have been caught. Although the attempt seems logical, it actually needs power against the net to push it down. None of the fish seem to touch the net at the bottom however and if it is the whole mass of fish achieving it, then the bottom fish should have been squashed against the net which (again) isn't the case. 'What brings the net down?' is the question here. (Done deliberately by Disney/Pixar to be visually aesthetically pleasing.)
Deliberate mistake: When Austin and Felicity cross the street when they are shopping, you can see green hills behind them, very much like Hollywood and not 1969 London. (Deliberate reference to an earlier joke)
Deliberate mistake: When the Trunchbull is drinking from the glass with the newt in it, you can easily see that she doesn't actually drink anything, as the water level stays exactly the same. Logical, as the newt is real, but it's still very obvious because she drinks for about 15 seconds. (00:46:55)
Deliberate mistake: After the trilithium missile hits the sun, it is shown going out in real time from Veridian III. As the planet is relatively earth-like, it is several light-minutes away from the sun. The filmmakers wanted it to be obvious that the missile was successful, so they ignored the speed of light. (01:20:35)