Visible crew/equipment: After Keanu finds Dr. Alistair Barkley dead on the lab floor and goes to attempt to revive him several shots show nobody else is around him, but straight after he starts to push on his chest a crew member can be seen stood over his right shoulder in a red top with a blue sleeve.
Continuity mistake: In the final underground laboratory explosion scene Keanu Reeves and Rachel Weisz are being pulled up to the surface in a cage by a crane on the surface and are covered with grey soot from the underground explosion. In the ensuing scene when being met by the people on the surface they are all cleaned up.
Audio problem: During the chase scene at the science museum, there is a shot where an FBI Agent reports on a disturbance there. If you watch closely, you can see where he originally said the "Smithsonian", and the audio was dubbed to say "science museum". (01:08:20)
Factual error: In a radio news voice-over shortly before the first chase scene, the newsreader comments that "Calls have flooded in from all over the world regarding Dr Barkley's research." He then goes on to mention that the Royal Academy in England has expressed an interest. The "Royal Academy" is more formally the Royal Academy of Arts. They probably mean the Royal Society, which is the most important scientific institution in the UK.
Continuity mistake: When Eddie is escaping with Lily from the museum he is on the right hand side of her but in the next shot of them he is now on the left. (01:04:45)
Factual error: In the scene where Keanu Reeves breaks into a house (after the snowmobile chase) he kicks a door in. When any door is broken down in this way, the lock either breaks or is wrenched out of the door. However, when the door swings shut behind Reeves, there is an audible click as the latch closes again.
Revealing mistake: When the policeman is shot on the roof of the observatory and the police cars drive across the grass, you can see the tyre marks in the grass from previous takes.