Continuity mistake: During the scene after 'Training', Alex is at HQ being told he will take the place of Kevin the 'computer nerd'. When Mrs Smith first hands Alex the Computer books in the wide shot, they are being held so that Alex can read the titles. In the close up shot of them landing in his hands, they are parallel to his body. Then, in the next shot, they are back to being the 'right way up'.
Continuity mistake: At the start of the movie, Ian Rider is killed by two bullets shot through his side window. The glass then shatters and forms the word, 'Stormbreaker'. However, when Alex spots his uncle's car in the breaker's yard, there are bullet holes all in the door. They were put in so Alex knew his uncle didn't just die in a car crash, but still.
Factual error: When Smithers (not identified by name in the movie) gives Alex his kit, it includes a fountain pen which shoots a dart filled with Sodium Pentathal. That's supposed to cause a person to do what Alex says. Sodium Pentathal is a form of barbiturate. Barbiturates cause impaired coordination, therefore it's unlikely that Mr. Grin could have flown a helicopter under its effects.
Visible crew/equipment: When Nadia Vole drives Alex through Port Tallon, there is a shot where you can see the filming crew in the radiator of the Hummer. This is mentioned in the filmmakers' commentary.
Continuity mistake: When Alex climbs out of the chimney in the house at the training camp, there are bits of straw on his woolly hat. In the next shot, they are all gone.
Continuity mistake: When Alex is tied to the chair and Sayle explains about his virus, Alex says "You're not being serious". The shot cuts to Sayle, who is putting a cigar in his mouth. In the shot immediately after it is a close up of Sayle and the cigar is gone.
Plot hole: Alex and Jack go to Liverpool St. Station to find the guys from Jeff Slater's. This is on the day of the funeral, otherwise it would make no sense going there. But when Mrs Jones sees Alex, she says "shouldn't you be at school?" This makes no sense because Alex would not go to school on the day of the funeral. It's not a character mistake because Mrs. Jones would never make that mistake.
Revealing mistake: After Alex has been pulled through the wall of the photo booth and is sitting on the chair waiting to move through the tunnels to MI6 headquarters, the wire used to pull the chair's platform along is plainly visible.
Continuity mistake: In the scene after Alex is captured, Darrius is doing a monologue with Mr. Grin and Nadia watching and Mr Grin throws a knife into the chair Alex is sitting on, impaling it above his head. All throughout the scene, the space between the knife and Alex's head changes between shots (and, no, it's not just Alex shifting in his seat), and after Darrius says, "Actually, it was a near miss," the camera cuts to a wide shot of the group and the knife is gone altogether.