Deliberate mistake: In the scene with the first demonstration of the digging laser, they dig/blast quite a hole in the mountain. Even assuming the laser can very easily shatter the rocks substance, still the debris would have to go somewhere, yet there appears to be none. And the amount of power needed to convert matter into energy is not practical.
Deliberate mistake: After the game has entered the real world, and Floop and Minion are there to "save the day", Carmen and Juni throws seven pairs of glasses to them. But afterwords, we see there are only four pairs of glasses on Minion and one pair on Floop, which totals five. (01:11:10)
Deliberate mistake: When Jar Jar gets arrested in the Gungan city, in the second shot of Jar Jar and Obi-Wan, Obi-Wan and a part of the floor behind him are reversed. This can be seen, for example, because two of the red areas on the floor have switched positions, and Obi-Wan's braid and lightsaber are on the wrong side. (00:14:00)
Deliberate mistake: In the shot near the end of the film where Donnie grabs the keys for the station wagon, you can see a Blockbuster Video member card in a cup. That card design wasn't used until the mid to late 1990's. This movie is set in 1988. Deliberate as it's a product placement, but still wrong. (01:37:10)
Deliberate mistake: The slow rate of the radio telescopes at the VLA has been greatly increased for the movie. They are actually quite slow and make little to no noise.
Deliberate mistake: Spoilers! When Black Manta is defeated, he is knocked unconscious and tumbles down a rock face after his helmet explodes on his face into the waters by the shores of Sicily. These currents and waves at best would have carried him to the rocks or the beach, leaving him on land or near it. However in the after credit scene he's somehow found out in the middle of the ocean on a broken drift wood. He would not have been carried back out to sea like that.
Deliberate mistake: There is just too much movement and detail in the synthetic skin masks. Peyton lost a large portion of his face in the explosion, and cannot make much expression with his own face, but somehow he can make the masks move perfectly just like a real face.
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: 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: The Fremen wear "stillsuits" to conserve their water, yet leave their heads completely uncovered. This would result in quite a bit of water loss through perspiration. (In the book, they wore hoods, masks and nose filters, leaving only the eyes uncovered, but it wouldn't work in a movie to have all the actor's faces obscured!).
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: 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.