After David teleports his father to the hospital, David's gray sweatshirt has blood on it. In the next shots, it's clean.
David rents room 256. In the next scene, when the manager knocks on the door to complain about the noise, the room number is 203.
When Griffin crash lands the jeep in the war zone, a man is sitting next to him. When Griffin climbs out, the man is gone.
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 Millie is talking to David about the places she'd like to visit, actress AnnaSophia Robb isn't wearing contact lenses, because her eyes are blue; in the following scenes, they are dark brown.
Big Ben, the bell in the clock tower of the Palace of Westminster, rings at 118 decibels. You could not stand beside the clock face and not suffer significant pain. 118 decibels is also on the threshold of immediate, permanent hearing loss.
A London taxi has a number on the wing. Aside from a plate at the back, London taxis have no numbers on the outside.
When Griffin stole the mercedes in Tokyo, the wheel of the car is on the left side of the car. In Japan cars have the wheel on the right side since they drive on the left side of the road. It's impossible that a car shop in Japan can sell car with the wheel in the wrong position.
In the closing credits, the song "Ahead By A Century," performed by The The Tragically Hip, is stated as written by Bobby Baker, Gord Downie, Johnny Fay, Paul Langlois, and Robert Sinclair. Robert Sinclair's credit should be Gord Sinclair.
A London bus is teleported and sounds its horn. The sound used is that of an American truck, not of a Routemaster bus.
From the age of 15 and being the child of a single-parent family, David jumped and then lived off the grid, yet somehow managed to have a passport for international travel to Rome. If he wanted a passport, he could have jumped home and found his birth certificate. He could use that to get a driver's license and then a passport. Nowhere is it claimed that he was totally off the grid.
The Paladins use electrical cables to nullify the Jumpers' abilities. How the Paladins did this prior to the widescale use of electricity in the early 20th century is never explained. Nowhere is it stated that they used modern weapons during previous centuries.
The main plot covers a few months, but various establishing shots of Manhattan show the Empire State Building lit for Independence Day and Christmas.
When David is talking to Millie at the bar where she works, an extra (a young woman) keeps looking at the camera and fidgeting.
When David is on top of Big Ben in London, the clock behind him shows 8:30, but it chimes as if it was 8:00 or 9:00.
When Griffin is perched on top of an adjacent building and looking down on the Colosseum entrance, a film crew, camera, and dolly tracks are clearly visible on 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.
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 David and Griffin walk out of the Tokyo subway station, the sign is for Ginza station, with signs for the Ginza and Marunouchi lines. When they get outside, they are in Shibuya, not Ginza. Furthermore, the Marunouchi line does not go to Shibuya.
When David is waiting for Millie to get off the plane at the airport in Detroit, he looks up at a very large arrival/departure board. None of the major airports in Michigan (including the Ann Arbor area) has such a board. This was clearly filmed elsewhere.
Jumpers are shown to be able to travel around the planet with a single "jump." How the Paladins, 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.
When he walks out of the police station after his chat with Mark, Roland states that "Millie boarded a plane to Rome 16 hours ago and she didn't go alone". How did Roland get that information? Mark couldn't have known. He was in a bank vault for the night and then in the police station interview room for most of the day.
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 makes a list of places to visit, she spells Prague "Prauge."
When Millie helps David with the cut on his face, the two each drink a beer. Millie is on shift as a bartender. While it is not illegal for bartenders to drink, most employers in the United States would immediately fire a bartender for drinking on the job.