Continuity mistake: When the three bride Autons attack Jackie, and they open their hands one at a time, it is clear that when the second Auton opens its hand, all three are already open. After it cuts to Rose, and back to Jackie again, the third one opens (even though we just saw it already open).
Revealing mistake: During the scene in which the Doctor is climbing the transmitter, there is a shot in which he is viewed from above and is then struck by lightning. In this shot, the Doctor's foot disappears briefly as it leaves the green screen on the ground under the actor.
Deliberate mistake: When Jack is scanning the gas mask people, he has a scanner on his right wrist. However, when he shows Rose and the Doctor his image of the Chula warship, the scanner is on his left wrist. The makers flipped the stretch of film, according to the commentary, to make the shot work.
Other mistake: When Miss Hartigan is testing the earpod control, the men start off facing her. She instructs them to turn to the right. They turn 90 degrees clockwise. She then tells them to turn to the left. They turn 180 degrees anticlockwise. However, they should have only turned 90 degrees anticlockwise, and end up facing her again. What they actually do is turn on the spot, as opposed to turning left. It takes a further instruction from Miss Hartigan for them to face her again.
Factual error: When the Doctor spots Rory taking a photo of Prisoner Zero, we're shown a brief close-up of Rory's hospital identity badge. The date of issue is given as "30/11/1990". The main body of the episode is set in 2008, two years before Rory and Amy's wedding in 2010. It's further established in the episode that Rory and Amy played together as children after her first meeting with the Doctor in 1996, with Rory observing that Amy made him dress up as the Raggedy Doctor. Rory could not possibly have worked for the hospital for eighteen years at the time of the episode.
Factual error: When Rose is locked in the room and the bodies come toward her, you can see a modern-day electric light-switch to the side of the door she's trying to get through. When the Doctor hears her screaming for help and runs for her, you can see a central heating radiator. In fact, the undertaker's house has at least two radiators in different hallways. Both are wildly anachronistic for the time period.
Revealing mistake: When Mickey closes the wheelie bin lid, he then finds the plastic stuck to his hands, he lifts his hands up and the plastic stretches like tar. If you look closely when he lifts his hands up for the first time, you'll see that a shadow of one of his hands is cast on his shirt, but there is no shadow of the strands of plastic stuck to his fingers. Additionally, when he turns around to pull away from the bin, he crosses the strands over each other, but they are still parallel in the following scene.
Character mistake: In an early scene with Yvonne Hartman, she says "We've just measured the ghosts' energy at 5000 gigawatts." There are at least two mistakes here: (1) watts are a unit of power, not of energy (that would be joules); (2) later on, when Hartman is showing the Magnaclamp to the Doctor, she refers to imperial tons and says "Torchwood refuses to go metric", but a gigawatt is a metric unit.
Revealing mistake: When the Doctor and Rose are talking at the bay, the Doctor's hair is blowing in the wind, but it's not when he is shown in the TARDIS. Considering the image of him on the beach is a projection of him in the TARDIS, the two versions should match. The actor was obviously on the beach recording his lines with Rose and back on a set doing the inside scenes.
Continuity mistake: When Mickey enters one of the school's computer rooms, dozens of pupils are busy typing, and every one of them is also wearing headphones. However, once Mickey unplugs the main connection for the computers, and shouts for the students to leave, when the students begin to get up, their headphones have instantly removed themselves from their heads and been placed neatly on the desks next to the computer keyboards.