Continuity mistake: At the beginning of the movie, the girl gets assaulted from the back: you see at first exactly from the shot from behind that the backpack she is carrying escapes her arms, but in the subsequent shot she is still holding it. (00:02:10)
Continuity mistake: When Nicolas Cage aka Frank Walsh first shoots a blow dart at Kevin Durand aka Richard Loffler he hits him in the left shoulder. Ten seconds later Kevin he pulls the dart out of his right shoulder. (01:23:15)
Other mistake: The opening (like most of the movie) does not make much sense, so you can pick your kind of mistake here; the special effects are cartoonishly bad throughout the big firework explosions. When John Abraham is knocked through a window by a rocket (which takes off with a 270° turn without even rising) to the face, he gets up unscathed and starts screaming for Junky and Chandu. The camera moves from them to him and he's running with the girl in the red costume in front of him (which was way behind, safely, when he crashed through the window, so already that is wrong), and then there's a wider shot. In that shot, you can tell that Adams is bumping into the same people as before and the distances between the extras are all wrong. (00:06:35)
Revealing mistake: Obvious use of green screen for buildings across the street. On and off, the background fades, and buildings appear higher or lower depending on the camera's angle. At one point, the angle of walls behind Rex (Bruce Willis) is at a downward angle, and his head is almost touching the ceiling. (00:06:10 - 00:07:25)
Character mistake: Casey is sixth of six male students standing in a row to individually demonstrate a karate move for Sensei. After the fourth student, Sensei passes up student #5 and says, "Next. Casey." Sensei completely missed the fifth student, the only other beginning white belt like Casey. (00:28:45 - 00:29:10)
Plot hole: SPOILER ALERT! During the final fight, Joey kills Frank and she reverts back to human form. Abigail tells her she's fine, because Frank was the one who turned her. However, when Frank kills Lambert he does not revert back to human form, even though Lambert was the one who turned him.
Factual error: This is set in 1966. The soldiers are all using the Aussie version of the M16 which was introduced in Vietnam by their military in 1967 with limited use and only became more widely used somewhat later.
Suggested correction: There's no such thing as an Aussie version of the M16, they were all made in the USA by Colt, or its contractors. I assume the poster means the M16A1, identifiable by the bolt assist lug on the right hand side and closed flash suppressor.
Factual error: Towards the end of the movie when Superman and Henshaw are fighting on the Watch Tower in space, Lois hits the sun shades to lower them so that direct sunlight can hit Superman and power him up. This is out in space with no atmosphere to filter the sunlight. The reason the blockers were there was for this reason, to keep the harmful unfiltered sun light from hitting people on the ship through the windows. However, she is able to stand there in the direct light after it's done and kiss and hold Superman without being hurt or burned by the intense direct unfiltered sunlight or its radiation.
Continuity mistake: After Wesley has intimidated the snot bully, he comes back home and finds the police. Sitting at the table, his mom holds his arm and says "Wesley, Mr. Chambers asked you a question." Mary Elizabeth Winstead has her right arm on the table, close to her body. Change of angle and she is holding the coffee mug instead. (00:45:10)