Deliberate mistake: As the Lotus drives off the pier and enters the water, the exposed underbody is that of a normal car. After it enters the sea, the underbody we see is completely sealed, which it needs to be to allow the car to submerge.
Deliberate mistake: When Alexander is travelling to the future for the first time, it shows a speedy acceleration of the events around him. However, the planes that are seen flying by are moving at normal speeds, or at least speeds way too slow since they should be moving too fast to even see, since skyscrapers are being built in a matter of seconds.
Deliberate mistake: While most of the German spoken in the movie is correct (even if with bad accent) there is a translation error in the scene at Yankee Stadium. The accent suggests that these bad guys were raised in the communist eastern Germany and previously served in the secret service "stasi." When the guy with the sniper rifle gets nervous and asks if he should shoot or not, the other one says,"Nein, wir brauchen den anderen", which would translate, "No, we need the other one", but the subtitles say, "We'll follow him", which they do.
Deliberate mistake: There is one scene in the movie where Heath Ledger reads a Latin sentence in a book. As he is translating the sentence, he goes over the words one by one with his finger. This would never be possible in a Latin sentence, because words in Latin are never in exactly the same order as in English. Words that actually belong together can be placed at opposite ends of a sentence.
Deliberate mistake: In the prom scene at the end, there is a shot of a couple dancing with his hand on her rear-end. A counselor comes over and hits the boy's hand to make him move it. He complies, they kiss, and he puts his hand back when the counselor leaves. The camera cuts away to a different shot, and then returns to an over-head wide shot of the crowd. Down in the lower left-hand corner you can see the exact scene with the couple and counselor being filmed.
Deliberate mistake: Charlie's room has a hole big enough for him to climb out of in the ceiling. I know it is to show just how poor the family is, but we see he has only a thin wool blanket for warmth. He would have frozen to death in his sleep during winter by now.
Deliberate mistake: Winners of the Nobel prize don't give an acceptance speech - they usually give a lecture before the award is given, and then at the most say "thank you," or in Nash's case "money would be nicer".
Deliberate mistake: When Alice jumps on the dog and they start running, her dress and her hand-band suddenly changed side. Probably they mirrored the image, and instead of going left as directed, it felt more accurate to go right.
Deliberate mistake: In many of the non-CG generated snake shots, what appears to be a very venomous coral snake is in fact either a scarlet king snake or a California mountain king snake (depending on the shot). These are much safer, non-venomous alternatives for filming with the actors. Look for the ordering of the colored bands (red/black=venom lack, red/yellow=kill a fellow).
Deliberate mistake: In the end of the NASCAR race, Tripp and Gordon get into a crash making Gordon spin, but he somehow is still able to come in second place even though every other racer was right on his back when he spun. He wouldn't have been able to regain that much speed in that short amount of time.
Deliberate mistake: When Carrie is hiding in the locker room to record John talking with his friends, it's clear that her camera is behind the vent, and the openings in the vent are closer together then the diameter of her camera lens, however we don't see the vent slats in the camera view or the replaying of the video footage in a later scene. Not to mention the fact that she isn't holding the camera steady. This is impossible.
Deliberate mistake: Main headlines in newspapers appear translated for each country for the kids to understand it, but the rest of the news appear in English, despite the movie taking place in Paris. Also, most signs -such as the poisons in the window shop- have labels written in English.
Suggested correction: By that logic, it's a mistake that the characters speak English. It's an American movie set in France, and like you said, it's a kids' movie. Everything is in English for simplicity's sake.
Deliberate mistake: In the scene where Forrest is describing his heritage, the clip of KKK on horses is taken from The Birth of a Nation. In this clip, you can see tire tracks on the dirt road well before automobiles were supposed to be in existence. Robert Zemeckis decided to leave this mistake in to perfectly match the clip to the original movie.
Deliberate mistake: During the movie, when Mulan is just a girl, you can see that her eyelashes extend beyond her eyes. When she is pretending to be a boy, her eyelashes are short (this makes perfect sense). But when she is in the medical tent her eyelashes are long even though she had no time to put on makeup. This is deliberate though, because without it she would have still looked like a boy, and just pulling her hair down wouldn't make her look any different (since that's how she looked in the pond). So they had to change her eyelashes to make her look more girlish.
Deliberate mistake: When Bullitt enters the hotel room to do a Recki, we see photos of the injured man on the wall. From this we can conclude one of two actions. 1: The ambulance crew took so long to arrive, the police had plenty of time to take a variety of photos from many angles. 2: The police did not let the medics in until they had taken their photos of a man who was in need of immediate medical attention. Wouldn't the injured man rather have his wounds seen to first than his photo taken?
Deliberate mistake: When Rocky cuts Drago during round two of their fight, the punch actually hits Drago on the chin. His eye would not cut from that impact.
Deliberate mistake: This was probably done intentionally to make them more visible, but the bullet holes left in the stairwell wall by Bart's handgun while he is chasing Danny during the movie's climax look to be about the size of golf balls. Typical handgun calibers aside, just looking at the size of the clip he's loading into the gun and seeing how many rounds it holds, those rounds would have to be much smaller than the holes the bullets made.
Suggested correction: It's a 9mm Glock18. The standard magazines have 17 rounds, the long ones 30. The holes could be larger because it's an old building and the plaster might break apart differently than modern drywall.
Deliberate mistake: After Carmen rescues Juni on the boat/sub, he accidentally re-engages the autopilot and they submerge. In the next shot as two Thumb Thumbs jump off their speedboat, the name, 'Donzi', that is written across the side of the boat, is backwards. This shot is flipped. (00:24:10)
Deliberate mistake: During the rumble scene there is a "Soc" whose clothes are completely dry and clean right before the Socs surrender. He's wearing a light blue shirt.
Deliberate mistake: During the chariot race, the chariots crash together but the arrangement of the horses make it impossible for them to actually collide. In some instances (particularly in an aerial shot as Ben Hur and Messala round the turn) it is obvious that they repositioned the shaft of the chariot to between the first and third horses instead of being in the centre between the second and third.