Factual error: The villain performs his hit at the beginning of the movie by remotely changing the GPS destination of a cab, so they head to the wrong place and into an ambush. Assuming that neither the cabbie or Pope notice the change on screen, and that his sophisticated software silenced the voice announcement of the course being recalculated, and makes the new place also marked as the old one (it is after all a god-like movie software), the trick is done on on a London black cab, whose drivers are notorious for "The Knowledge", aka being required to learn the entire topografy of the city in one of the most demanding training courses in the world, and not using GPS. It'd be definitely unlikely for the cab driver to be totally unaware, to the point of Pope himself noticing first that they are at the wrong place.
Factual error: Jan Strook is a Dutchman; throughout the movie he is referred to as "Jan Strook", which rhymes with "took," when it should rhyme with "broke." This is even worse considering he has a Dutch accent in the movie, which leaves him no excuse for mispronouncing his own name.
Factual error: When Kevin Costner plunges off the bridge in a taxi, he cuts his leg on a piece of the door side glass. This is impossible as all side windows are made of tempered glass that completely shatters, leaving no sharp pieces that could cut.
Factual error: When the helicopter arrives at Dover AFB carrying Jericho, the controller states runway 22L. Dover AFB has intersection runways 1/19 and 14/32 and no parallel runways.
Revealing mistake: When Jerico is having his surgery the angle of the device that will be transmitting the memories is inconsistently angled in the real shot versus the monitor image.
Factual error: Showing the submarine Strook "hacks", the movie displays "USS Virginia SSN743." USS Virginia is SSN774, while SSN743 is USS Louisiana. (01:13:10)
Plot hole: Jerico leaves Jill's house to go to the university, driving her car. While he's away, Elsa pays her a visit and extorts the location. When we see Jerico at the university, he enters the book cellar, finds the famous duffel bag almost immediately, and as he exits, outside there's Heimdahl sitting there, having set him a trap. That would already been hard to swallow, but we could assume his location was significantly closer than Jerico's to the university library and Elsa phoned him. But becomes downright impossible when we see that to pull the lever of the Home Alone-ish trap there's none other than Elsa, miraculously arrived at his destination despite him having a huge headstart.
Plot hole: The CIA is desperately trying to find Pope's contact, to the point of doing the crazy experimental brain surgery shipping over the ocean the one scientist that may perform it, and an inmate. But they don't have Pope's house under surveillance or his phone tapped, so they have no idea Strook called him. The fact that Strook not hearing back from Pope would try to contact him was quite literally the most obvious possible event. (00:31:00)
Factual error: The bad guy's henchwoman reads the license plate as "SI52JGN", he repeats it as such but on screen he types "S152JGN" (with the second character as a number 1 and not a letter I). I (like Q and Z) is a letter that can't be used in the first 2 digits of a UK license plate, anyway. (00:04:45)
Continuity mistake: Jerico turns his back to Jill in the basement, telling her to go feed her daughter. She has second thoughts and points the gun at him. Costner is shown leaning on the column to his right, but he's leaning on the left one in the next shot. (01:11:55)
Continuity mistake: Bill Pope just went off the stolen bike and is descending the stairs to the tube; people around him change completely between shots (he moves past a short haired woman dressed in black that is a few steps ahead of him, too). (00:03:50)
Continuity mistake: Jerico causes the car crash to happen, and one of the agents is propelled out of the car through the windshield. You can see him roll on the asphalt at distance. In the rest of the scene his body is at an angle and on the foliage. (00:34:15)
Continuity mistake: When the Dutchman gets shot in the head, his laptop is completely open, 180° like a book. In the previous part of the scene, and when later the CIA agents hurry in, the laptop is open to a more traditional 90-ish degree. (01:31:35)
Factual error: Jerico is transported from Hazelton penitentiary, West Virginia, to the Air base in Delaware, on a helicopter with a registration number starting with G, therefore a UK aircraft (where the movie was actually shot). (00:14:00)
Continuity mistake: Jerico comes out of the fish 'n chips place with food and a coke. A cyclist is travelling along the road. In the next shot a passerby that was not there before is behind him, and the cyclist is passing again. (00:37:10)
Continuity mistake: Jerico is carried into the operating space. Look out for the nurse that is holding the bed by the lever on the bottom left corner; she is using her right hand to pull, then her left hand in the next shot. (00:20:20)
Continuity mistake: When Pope messages his colleague from the cab driver's phone, the time on display is 13:49. When the phone is used as GPS to get to the destination, there has been a sudden jump and it's 14:57. (00:05:10 - 00:05:55)
Continuity mistake: After losing Jerico at the bridge, Elsa brings a bowl of nuts to Xavier Heimdahl. The bowl has a nutcracker on top, which changes place after he shouts at her and goes back where it was at the end. (01:07:00)
Continuity mistake: When Emma is teaching Jerico some notes on the piano, she tells him "Put your hand there", but said hand is the left in the close-up, but the right in the shot that immediately follows. (01:16:50)
Continuity mistake: When Elsa points a gun at Jill in the bathroom, she is holding the gun diagonally with the camera on her left, straight in the shot from the right, and it switches back. (01:22:40)