Deliberate mistake: Father Merrin says, "It is He who commands you", and we hear and see the ceiling crack above his head. In the next shot we see the ceiling above him and they are no cracks in it, but four shots later we see the exact same spot and now cracks appear even though we hear no more cracking over-dubs after the first one. (01:49:15)
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: 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.
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: In the scene where the Punks follow the Warriors into the bathroom, Rembrandt sprays the head punk with his red spray paint. However, the spray coming out of the can is clear, not red.
Deliberate mistake: In a lot of the shots in the cockpit, when Teri is attempting to begin taking control of the aircraft, notice the Horizontal Situation Indicator on the First Officer's side. The compass rose is moving around erratically - which would suggest that the 747 is also changing heading extremely erratically and robotically - which isn't possible.
Deliberate mistake: When Boyd has saved the Vice President's life after chucking him into the water, Boyd looks down at the VP who is being dragged out. Suddenly, there is a picture taken that appears in papers, but there was no press or person on the bridge where Boyd is with a camera, so where did the photograph come from? (00:06:55)
Deliberate mistake: When Bond is fighting Zhao in the clinic, they accidentally set off the tomograph Zhao was lying in. As this machine's powerful magnetic fields indeed would pull any metallic object in, no doctor with common sense would allow sharp objects and other stuff within range. You aren't even allowed to carry watches and have to report any dental fillings. (00:43:50)
Deliberate mistake: In the scene where they break into the train from its roof, you can notice that despite the high speed and the consistent wind, Captain America's fellows have no difficulties in running, standing up still, and even jumping, like they felt no air resistance. Moreover, you can see that their hair is not moving at all, completely missing to realize any "windy" effect.
Deliberate mistake: Polly's and Sky Captain's clothes are discarded because they are contaminated with uranium; however, Polly gets to keep her camera. Her camera would have been contaminated with uranium, too, because she had it with her in the underground cave.
Deliberate mistake: At the end of the film when Pacino and the gangsters are shooting each other on the escalator, the escalator takes a long time to get to the bottom, way too long.
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: As Nancy and her Mum are leaving Rod's funeral, you can see the shot of them leaving the funeral has been sped up. Watch the Volvo "jerk" as it pulls away as the speed is rapidly increased.