In the scene where David and Millie are stopped by police outside the Colosseum, the officer puts one hand out to stop David and one hand on his holster as if to draw his firearm, only there is no firearm in his holster to grab.
When Millie is talking to David about the places she'd like to visit, actress AnnaSophia Robb isn't wearing contact lenses, because you can notice her eyes are blue, and in the following scenes, they are dark brown.
When David returns to Millie's apartment to rescue her he jumps to her balcony where her shades are completely drawn. In the next scene they are open enough for him to see in to jump into the apartment where he is immediately attacked by a paladin entering from the balcony David had just been on.
During the Detroit Airport scene, a sign can be seen briefly in the background saying "Welcome to Prague Airport". Additionally, on the shot of the arrivals board, the words "time" and "destination" are visible written in Czech. Some of the destinations shown are also only small European airports that would not host transatlantic flights.
When Griffin is playing video games in his lair, he is clearly using an X-Box controller and the game he plays appears to be Halo, an X-Box exclusive game. Later, when he's looking through his game collection, the games are clearly PlayStation 2 titles.
When David teleports to the school library while his father is trying to open the door, his father closes the bedroom door when he leaves. When David teleports back to the room, the bedroom door is open, and David closes it again.
When David and Millie are stopped by the Italian Police outside the Colosseum as David turns to leave you can see the officer on the right begin to draw his weapon and a gun being pointed towards David as he tries to apologize to the docent. Yet in the following shots no officers have weapons drawn until David asks to be let off with a warning and the officer once again draws his weapon, this time with the sound effect.
When Griffin returns to his lair after dropping a Paladin in the Atlantic, he splashes David's shirt with water. The drops disappear when he walks up from the subway in China, and reappear when he walks down the street.
During the safe-chasing scene, it is daytime in Giza, Abu Dhabi, Chechnya, Manhattan, and Ann Arbor. That's possible some times of the year, but at the same time, it's night in London, Rome, and at Griffin's lair in Egypt.
Jumpers are shown to be able to travel around the planet with a single "jump." How the Paladin's which are alleged to have existed since ancient times are able to follow them is never explained. How they were able to follow them before the invention of modern transportation would have been impossible.
David teleports himself, Millie, Roland, and part of Millie's apartment into a lake, then into the library. Afterward, he teleports himself and Roland to the Grand Canyon. When he leaves Roland behind, his clothes are completely dry.