Factual error: When Alex shoots Jessie in the chest, the blood is pouring out of the hole in the trench coat. Gravity would be doing that between her skin and red sweater instead. (01:35:15)
Revealing mistake: After the woman is strangled and the people come in trying to find the little kid, the dead woman is clearly seen blinking. (00:11:25)
Factual error: As the kidnapper is watching TV, we hear a news anchor describing the kidnapped child. She is described as 12 years old, 3 ft. 5 in. tall, and 52 pounds. This is the size of a child half this age. A 12 year old of this size would be freakishly small, which this character is not. And as we see her throughout the movie, she is easily approaching 5 feet tall and in the 70 - 80 pound range. (00:13:30)
Continuity mistake: In the opening scene where Alex's partner is in the car with the bad guy, when she pulls her gun and he hits the brakes sending her into the dash she is not wearing a seat belt. Immediately after, when the car goes over the side of the dam, the shot looking down on her shows her with a seatbelt on, the reason she didn't fly from the vehicle. (00:04:10)
Suggested correction: She's wearing a seat belt at 00:03:50 when he's trying to get some top from her. He's pulling on her head and that's when he finds the Bug in her ear. And you can see she's wearing a seat from 3 mins to the time she's hanging from the bridge in the car. 00:03:50-00:04:11.
Suggested correction: I just rewatched - she is wearing her seatbelt when he slams on the brakes, and she hits her head.
Factual error: When Alex & Jezzie are on their chase throughout the city they end up at Union Station. The scene is really filmed at Union Station, however when they go downstairs to get on the train, as instructed, they are no longer really in DC. The train used is not DC's. Platforms are not marked by letters or any other designation in DC and the interior of the train car (layout of seats etc) is that of Baltimore's, rather than DC's.
Continuity mistake: Towards the end of the movie, Jezzie is shooting through a door, trying to kill Megan. She has a black Glock pistol. When she reloads the gun, it magically becomes a silver Smith & Wesson pistol. Then, when she walks up into the loft of the barn, the gun again is a black Glock.
Continuity mistake: When they are in the classroom and the lady is on Megan's computer and says to Alex to come there and look, he is in front of the teacher's desk but when it pans back to Alex it shows him walking around the back of the teacher's desk and down the far side of the room. Why not just walk down the main isle where he was at? (00:31:30)
Continuity mistake: After Freeman and the Main Detective girl are at the beach looking at the body of the man who was shot in the water trying to save the little girl, Freeman says "let's go back to the city". On their way back in the car, of the three times the camera is on him, he only has his seat belt on twice. (00:50:00 - 00:51:00)
Continuity mistake: When Morgan Freeman starts his chase to leave the diamonds for the kidnapper, the streets are wet with rain. About 5 minutes later, as the female character is filmed following him, the sun is out and the streets are dry.
Continuity mistake: At the beginning of the film when Freeman's partner shoots the guy in the Corvette and the car starts flipping, the right front tyre is shown coming off the car and tumbles in the air several times, but when the car is finally getting tangled in the guard rails, it shows the car with still 4 tyres on. (00:04:15)
Factual error: The 'game' set up by Soneji is a whole bunch of computer science-fiction nonsense seen only in movies, with the common factual error of blurry pictures that can somehow be zoomed in ad libitum. The IT agent comments when Cross has clicked on a picture from the camera recording of the class; "Dr. Cross isn't in cyberspace anymore! You're at a live site, looking through a video camera", which does not even make sense. The sequence that follows is not a camera feed, with a real camera being moved, but a panoramic composite shot of the room.
Continuity mistake: During the "running game" segment, Cross gets a cell phone that uses an earpiece and is told to keep it (for further instructions). When he gets to the subway loading platform, he gets another call, but he is not wearing the earpiece while he listens to the new instructions. Soon after that he is shown wearing the earpiece again while he listens.
Suggested correction: You probably haven't focused on Morgan Freeman's ear. The cord of the earphones are hard to see in that sequence and you may be led to think the whole apparatus is gone, but if you just look at his ear you'll see that from the entrance to the escalator to the platform to the train, in every part of the conclusion of the 'running game' happening in the station, Alex Cross is wearing the phone earpiece.
Continuity mistake: Morgan Freeman is sent off on a race on foot to various locations around the city and given a time limit to arrive. The addresses of each of the spots he must be at in a given time period are listed, but based on their locations, there is absolutely no way a person could get from one location to the other in the time given. There was a considerable amount of backtracking and it just wasn't possible, especially the last bit, from 12th and Madison to Union Station, 1.5 miles in 4 minutes.
Continuity mistake: When Morgan Freeman is talking on the phone with the kidnapper, he says (referring to Megan), "Do you have trouble saying her name?" Two minutes further into the movie, in the car, when he plays back the tape of the conversation, he is heard to say "Do you have trouble saying THE name?" (00:16:25)
Continuity mistake: After Morgan Freeman shoots out the train window to toss the diamonds out, the hole in the glass gets larger, enough for him to stick his head out easily. (01:10:00)
Plot hole: The kids in Soneji's class use an encrypted GIF algorithm to pass notes to each other and that "drives the teachers crazy", since they are unable to catch cheaters that way. But how do they do that? Easy, they have a message system in place installed on their workstations, that warns them with a big pop-up that they've got "A new message"! It would be easy to sanction and prevent the cheating by simply removing the chat application, no matter if they use it to chat directly or pass Michael Jordan photos as shown in the movie, which they have no business doing during an assignment anyway.
Continuity mistake: In the scene where Alex and Jezzie are waiting for the kidnapper to show up to get the president's son, Alex says that Jezzie can smoke. She proceeds to roll down the window and light her cigarette. When the camera pans back, the window has been rolled up.
Plot hole: With over two years spent teaching at school, nobody (students, coworkers) ever noticed the rubber face and rubber hands of 'professor Soneji' - and he teaches computer science, having to get close to people constantly looking at their screens and interacting with them - as shown in the classroom scene. Nothing is also said about the name being an alias and how he managed to teach to the super-elite school where daughters of senators and the Russian President (what is he doing attending middle school in the US anyway?) with no credential, or fake ones (the degree shown is in Mercusio's name). You'd think the vetting for the staff there would be iron-proof. He has also been wearing a fake gut, and something like that would have easily showed up if he ever got as much as a pat-down, which at a place with security so tight, is certainly a possibility.
Plot hole: Jezzie has files about Dimitri in her computer and is the one who asks Cross to do the stake-out at the embassy. She knows of Soneji's plan to kidnap the Russian kid, but wants it to fail, since she is more than content with the millions of ransom for Megan. This part does not make sense on any level; she can't know on which day Soneji is attempting the kidnapping, and since she and her accomplice know where he is hiding (or else they wouldn't be able to grab Megan from him when he is away), by all means they should have killed him rather than run the huge risk to let him try to kidnap another kid at the well guarded embassy and have him killed or worse, captured, before they can do their scheme replacing him. For their plan to succeed, Soneji needs to be dead, so he won't mess up for his delusions of grandeur.
Plot hole: Cross says that the best strategy to keep the kid alive is to pamper Soneji, stroke his ego and make him a living legend as he wants to be. What Soneji did though, was guide them to his real identity and name, since Soneji is just a front he used to be employed at Cathedral School, and in the first conversation with Cross he said about the Soneji name "That'll do for now." It's obvious to anyone then that he wants his real name and self to emerge from obscurity and drop the alias, and if Cross really wanted to please the kidnapper, he should have used his real name, Jonathan Mercusio. Despite these clear elements, that name is never used or referenced in the movie again.