Continuity mistake: Jezzie pours the diamonds from the thermos into her left hand. In the close-up, she is pouring them again. (01:25:30)
Continuity mistake: Jezzie's computer that she used for all her operations has the screen seemingly turned on, always of a bright blue even before Cross actually switches it on. When he looks at the password screen with just 'Administrator' as username, the screen is black, like it is not in any other part of the scene. (01:27:40)
Character mistake: Amongst the material collected about Cross in Jezzie's computer, there's a big magazine article related to the case of the previous movie "Kiss the Girls." The article writes in a huge font the title "The CASSANOVA killer." Not a very good magazine, misspelling Casanova like that. Incidentally, her notes also get the word "Temperament" wrong, missing the 'a', and she has a folder called "Dimitiri", getting the name of the Russian kid wrong. (01:28:30)
Plot hole: In her plot convenient computer content, Cross finds the address of the house for lease Jezzie has. The house is located in Lovettsville, Virginia. That means it's over one hour away from the apartment in Washington. If we take at face value what happens in the movie, with Cross breaking into the house once Jezzie has killed Devine, then it's impossible he made it in time to catch her and save Megan. One wonders what took Cross so long anyway to get to the house considering he visited the school that tipped him off about Jezzie when students were still around, and why he does not warn the authorities (which is kinda hilarious since what tips Megan off about Jezzie, is that she came alone, exactly what the hero does!). The timer on the computer screen when Cross finds out is 00:00:00, which is a bit unlikely and not much help. (01:29:00)
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)
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 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.
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.
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.
Plot hole: From a logistic and tactical point of view, the whole police/FBI operation revolving around the diamonds does not make any sense. The agents are supposedly spread around and in great numbers, but everyone is simply chasing him, while Cross is speaking freely through the radio and shares the addresses and instructions so they should be -ahead - of him, they know where he is going! Although, during the action, Cross tends to speaks directly with Jezzie all the time, as if all the other dozens of agents did not exist. Jezzie's presence itself is completely illogical, too, since Soneji ordered that nobody would follow Cross or he will kill the girl, and Jezzie is the one agent that he knows (she's been the kid's bodyguard for 2 years!) and is sure to recognize. She should be nowhere near the chase, but nobody objects at all.
Other mistake: Megan is kidnapped during the lunch break, and when Cross reaches the Rose residence, his friend from the FBI tells him about the forensics exams not netting any results. When he gets to the crime scene the day after, though, it's swarming with feds who are still doing things like checking the computer stations and even photographing the chalklines of the strangled woman, all sort of investigations that you'd expect to have happened already in the previous 24 hours or so.
Factual error: During the movie, Senator Rose's daughter is protected by the US Secret Service. A plot point also sanctions that senator Rose is basically a nobody, he does not hold important roles, nor he was threatened in any way before the fact. His daughter would not be under Secret Service protection then, since it is reserved only to the highest elected officials of the nation, not every single relative of every single House member.
Revealing mistake: There is a mistake in the (quite dodgy) CGI when the car tumbles down into the dam in the opening scene. At one point, the camera cuts and we can see the car bouncing downwards through the air, and there's a splash of water from where the car bounced off the wall of the dam. But if you pay attention, the splash of water simply vanishes/fades away about two seconds later. Sure, if it was more of a fine mist, it'd make sense that it'd lose visibility, but these were huge streaks of water that should still be visible for quite a bit longer.