Deliberate mistake: When the girls all order their food at the drive through they get their food but never pay. (00:17:15)
Deliberate mistake: In the fight scene with the chariots Maximus takes one of the horses from a chariot and jumps on it. The horse already has a saddle complete with stirrups despite the fact it was pulling a chariot and not carrying a rider. (01:23:30)
Deliberate mistake: In Paris' death scene, he blows alcohol onto his torch that illuminates the creatures around him. However the area is still illuminated after the light from his torch has disappeared. (01:12:05)
Deliberate mistake: When the Evo crashes into the tanks it jumps into them at height but there was nothing there to make the car jump. (01:17:25)
Deliberate mistake: Elizabeth Shue uses a drawer handle as an electromagnet. OK if it's really a magnetic material but lab furniture is generally made of aluminium or stainless steel which is not. There is no way that they would use an iron handle in a potentially wet, and hence corrosive, environment such as a freezer.
Deliberate mistake: You might be wondering where Terry suddenly comes up with Jolly Jack all of the sudden after escaping the lab. In the commentary, they say that the Joker, in his transmission to Terry in the lab, was supposed to be eating out of a candy jar with "Jolly Jack" on it, but couldn't have it due to time constraints.
Deliberate mistake: In the Director's Cut (the version most readily available on DVD), there is literally an entire 15-second chunk of the final fight that is repeated twice within 60 seconds. (It's the bit where Duncan and Kell are fighting on the ground, Duncan kicks Kell, then Kell kicks and slices Duncan) It's impossible not to notice, and it's not they're flashing back to what just happened... they just repeat the same 15 seconds of footage, add different sound effects, and assume people won't notice.
Deliberate mistake: Some of the text in this movie is in English, but some is in Japanese. Most noticeable when Tai writes the letter to Sora.
Deliberate mistake: In the scene with all the coffins and new Skull "recruits", Lucas knocks on the unopened coffin and Caleb pops up. The next shot is a wider shot that shows everyone standing around Caleb's coffin, but the guy in the coffin is not the actor playing Caleb, but a stand-in.
Deliberate mistake: The Americans actually spoke with American accents, but these very new Americans were British in origin, and so they couldn't develop a new accent in such a short time. The Americans should still have British accents. This would have been confusing and is done for the viewer's benefit, but still a mistake.
Deliberate mistake: In the scene near the end of the movie when Trigger is in the bilge trying to stop the air leak, the concussion of an artillery shell fired from the destroyer shakes some pipes loose. The mistake is that one of the flanges visible on a section of pipe has no bolt holes, making it impossible to join that pipe to anything.