Deliberate mistake: In the final shot of the film, Jill's head moves slightly when she's supposed to be dead. In the commentary, Wes Craven confirmed this wasn't strictly intentional, but he decided to leave the take in on purpose in case he decided to bring her back in a future installment. But unless a sequel proves she's still alive, it's technically a mistake, albeit a deliberate one.
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: After pulling the e-brake in his car (Mustang) and turning completely around during a chase scene, "Driver's" vehicle continues to shift gears as he drives in reverse at high speeds.
Deliberate mistake: Throughout the film, Babydoll's shoes will go from her heels to some kind of flats during high-action scenes.
Deliberate mistake: Right at the end of the film, the two Norwegians (Lars and Matias) are seen chasing after Lars' dog in a helicopter. Notice how their clothing and the interior of the helicopter are not the same as they looked in the original 1982 film by John Carpenter. It's supposed to be the same event.
Deliberate mistake: Before Nathan and Karen jump out of Dr. Bennett's car, Dr. Bennett's car is shown taking a sharp turn (close to 90°) and then speeding down the short but steep road. At a high speed, the car should have reached the level road within a second or two. However, Dr. Bennett talked to Nathan and Karen for a longer period of time. When the next exterior view of the car was shown, it was just reaching the intersection and straightaway. The car should have traveled a much greater distance than shown. (00:44:50 - 00:45:59)
Deliberate mistake: This mistake was admitted to in the DVD commentary by the director. When at the embassy, once they open the window, the camera pans up to show a destroyed helicopter on top of the building. This is a mistake as in Moscow, it is restricted airspace for helicopters, with none at all for any purpose to be allowed to fly over the city, not even to land on the American Embassy. However, the director really wanted the visual of a destroyed helicopter on top of the building so added it anyway. (00:41:49)
Deliberate mistake: The agent is entering the office approaching his desk where a computer sits with the screen on depicting classified material. Computers left unattended go dark after x amount of time. This computer being in a federal FBI building should be logged out of and not open for everybody to see. (00:19:00)