Continuity mistake: At the press conference, McArthur is going full "no comment" about pretty much anything. A grim Alex Cross is standing there. Next to him are the senator's wife and the senator. At the cut the senator disappears, leaving just the wife and the FBI agent. (01:11:10)
Continuity mistake: Cross is talking with Jezzie in her apartment, holding several sheets. The sheets are at the same height in a certain camera angle (when he says "You do what you are", and then "you were born with a gift"), despite the fact that meanwhile he moved those sheets around. (01:12:10)
Continuity mistake: After Mercusio gets shot, Cross has to face the senator, who tells him "and you're telling me you haven't a clue?" The agent walking past is nowhere to be seen in the reverse shot that follows. (01:19:00)
Continuity mistake: After Mercusio's home invasion, Jezzie's ice pack turns around in her hand between shots (you can make out of the way it is pointed in the first shot when the paramedic is still checking on her; some letters are visible at the end, and they are turned straight). (01:19:40)
Continuity mistake: Devine's cigarette burns half an inch the moment he turns the TV off (and we switch to the close-up). (01:23:05)
Continuity mistake: Jezzie points the gun at Devine's throat. When she begins laughing, she lowers the gun, which is still all the way up pressing to his jaw in the reverse shot. (01:24:00)
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)
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.
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: 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.