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.
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.
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.
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: 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 Hellboy is walking at one point, holding his gun up in his left, gloved hand (just after one of the agents has said "This place is like swiss cheese"), watch the frame. It switches suddenly so his right hand (the stone one) is his left, and he's holding the gun in his "right." (00:59:40)
Factual error: When they're first entering the whaling camp, a penguin startles Miller. That penguin was a black-footed penguin, which is a bird native to much warmer climates. If that little guy had actually been in Antarctica, he would have died within minutes. (00:20:40)
Factual error: One sweep through the town shows a Dodge Durango in a parking lot. The movie takes place in 1988; the first Dodge Durango was the 1998 model, ten years later. (00:34:15)
Factual error: During the Christmas season (December) Travolta and Phoenix discuss a transfer to an aide's position. That same night Phoenix discusses the possibility with his wife - with crickets chirping away in the background. Not in Baltimore in December.
Continuity mistake: In the Moscow car chase, Bourne's car is hit from the driver's side by a patrol car. The driver's side window breaks. In the next few shots, you do not see any broken glass on Bourne. In the very next shot the car is not damaged on the driver's side. (01:25:25)
Revealing mistake: In the bike scene you can see that the intro biker is much smaller than Belle.
Factual error: After the scene where they fall over the waterfall, and go through what they have left of the equipment. Bill, the Latino doctor, holds up the CD-reader from a desktop computer and says that the hard drive is broken, which would be OK if he actually had the hard drive present. (00:34:35)
Continuity mistake: When Vince leaves the freezer and is making his way onto the elevator, he is carrying a Baretta model pistol. When he shoots as the elevator doors are closing the camera cuts to a Glock model pistol, then back to the Baretta again. When the elevator reaches the upper level, the woman picks up the remains of the backfired pistol and it is back to the Glock. (01:21:15 - 01:24:30)
Continuity mistake: When Chris and Dani are at the police station and about to have sex, her shirt mysteriously reappears. They are kissing and Chris is shown removing her shirt (leaving her in a red bra). A few seconds later they are still kissing, and you can see that her shirt is back on. (00:58:55)
Factual error: I normally wouldn't bother with this sort of nitpicking, but this film specifically claims to be historically researched - and it's full of historical blunders. For a start, the film is set as the Empire withdraws its last troops from Britain - which was in 407 AD. Now Artorius Castus was a real Roman officer who really did command Sarmatian foederati at Hadrian's Wall, but he died around 200 AD. Cerdic was a real Saxon warlord who did go raiding the Britons with his son Cynric, but he did this in the early 500s. Pelagius really was tried for heresy, but he was acquitted and died of old age; the trial was a decade after this setting, and in the fifth century you couldn't be executed for heresy anyway. Also in the fifth century the Pope had no authority over Imperial troops. I could go on and on but that will do for now.
Continuity mistake: Towards the end of the movie, in the scene where Anna is taking the werewolf cure to Van Helsing and the vampire bride stops her on the large fallen pillar, she falls so she is in a sitting position with the cure in her left hand. She then switches it to her right. Then in the close-up shot, the cure is still in her left hand and she switches it again. (01:49:50)