Factual error: As Ben is clinging to the staircase while it is falling apart, there is a close-up of a nail being pulled out of the wood. This nail is round-headed, rather than square as it would have been over 200 years ago. It's also shiny instead of rusty, which indicates that it's galvanized. Galvanization as an industrial, metal-preservation process was not patented until 1837, and was not used in building materials until well into the late-1800s. Since the film states the staircase was made by "the Founding Fathers, " and there was no galvanization of iron nails in any industrialized nation in 1780s-1830's, this is a huge anachronism.
Plot hole: This film is set in 2004. The thought that no search and rescue operations would be put in place after an aircraft disappeared from radar during a routine flight is absurd. The Chinese are paranoid about intrusion on their territory and the downed aircraft would have been located by a simple satellite search within hours of it crashing. Chinese military satellites crisscross the Gobi and they are equipped with optical cameras, microwave and infrared detectors and radar, so spotting a metal aircraft on the ground would be simple even if it was hundreds of kilometres off course. The crew would have been visited by Chinese military helicopters (and probably arrested!) as soon as the storm had died down.
Other mistake: At the end of the film when they arrive in NYC looking for the library, we know that they survived because they are inside with a roaring fire burning. But where is the smoke up above, as Jack Hall approaches? There must be a chimney, or else they would have all died of asphyxiation.
Plot hole: Harry tells Doc Ock that in order to find Spider-Man he must find Peter first. Doc Ock finds Peter with Mary Jane in the cafe and throws a car through the window straight at them, then later throws Peter against a brick wall. Any normal person would've been killed instantly (or very badly injured), and Doc Ock doesn't yet know that Peter is Spider-Man. Given that Peter is his only lead on Spider-Man, it makes no sense that Doc Ock would try to kill him.
Continuity mistake: When Malfoy and his friends bother Ron and Hermione, Harry shows up and messes with the three boys. He grabs hold of Malfoy's feet, lifts them in the air and pulls him across the snow. In the first close-up of the soles of Malfoy's boots, not a speck of snow is on them, though he was just walking in it. Then in the next close-up, his feet still in the air, the soles are now covered in snow. (01:02:45)
Visible crew/equipment: As Sam and Rhonda have Fiona's car confiscated, when Fiona runs out shouting, "I can pay for those parking tickets!" the crew's black mat is laid out on the walkway, but in the overhead shot when she tries to run away that mat is gone. (Visible on fullscreen DVD.) (01:28:10)
Visible crew/equipment: As Achilles' ship nears the Trojan shores, Agamemnon snidely asks, "What's the fool doing? He's going to take the beach of Troy with fifty men?" At the start of the next shot, as the camera begins to pan down, on the far right, just beside a person's (who is dressed in blue) head is a metal bullhorn (ie. used to give instructions to cast/crew, and which definitely doesn't belong in this time period). (00:36:35)
Continuity mistake: In the scene where Cady is chasing Damien's car and talking to Janis, when Janis says 'he still doesn't want you' two extras in dark clothing walk up a pathway behind Cady. However when the shot cuts back to her, they have totally vanished. Even though they were wearing dark clothing, you'd still be able to have seen them, and there was not enough time between the different shots for them to have walked into the house.
Continuity mistake: The hull numbers of the Constellation change throughout the film between CVN-74 and CVN-68.
Continuity mistake: When Hutch tackles Starsky to the ground after his gun goes off in the disco, Starsky's badge falls to the ground beside his head. Hutch grabs it and holds it up, telling people to calm down, but when the shot returns to Starsky the badge is still there next to his head. (00:49:40)
Continuity mistake: When Napoleon is waiting while Rico makes a sale, he checks his watch to see how much time he has before the dance. The first time he checks it, the date on the watch indicates Thursday July 17. When he checks it again a few minutes later, it shows Monday July 21.