Continuity mistake: When Rose presents her mother with the Bazoolium, she's holding it in her left hand. When the view switches to look at Jackie, it shifts to Rose's right hand and then immediately back to her left when the view restores to the original vantage point. (00:02:45)
Continuity mistake: When Yvonne Hartman is showing the Doctor through Torchwood after leaving the TARDIS, she goes to push a door open into the main building with one hand, but when the camera cuts to them entering the building she pushes them open with two hands. (00:20:10)
Continuity mistake: When Yvonne is taking the Doctor and Jackie to the Sphere Room, there is a sign opposite the door that has the words "Torchwood Institute". In the next shot where you can see the corridor from inside the Sphere Chamber, the sign has disappeared. It reappears again when Rose is going into the Sphere Chamber, but this time it has directions to the Reception, Canteen and Lever Room as well as "Torchwood Institute". It also disappears again when you see the corridor from inside the Chamber. (00:23:30 - 00:31:45)
Continuity mistake: When the Doctor uses his sonic screwdriver on the glass partition in the Torchwood Institute, cracks radiate out in a star pattern, meaning the glass will break into pointed shards. When it does break, it breaks into cubes, like safety glass. (00:29:30)
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.
Continuity mistake: When the Sphere Chamber is first shown, there is a rolling staircase set up just below the Sphere. Rajesh Singh is shown climbing the staircase and nearly touching the Sphere. However, when the room is next seen, when Raj hears that the Doctor is coming and walks up to look at the Sphere again, the staircase has vanished. Later, when the Doctor and Jackie are shown into the room while Yvonne gives them the Torchwood tour, the staircase is still missing, and it's more obvious that it is no longer in the room. It does not reappear for the remainder of the two-parter.
Continuity mistake: After Pete tells the Doctor that Mickey went ahead because he wanted to find Rose, the Doctor asks him if he knows that Rose is his daughter from a parallel universe. The problem is that in Pete's last scene in "The Age of Steel", the Doctor saw Rose call Pete "Dad", leading to Pete departing in a hurry. (00:15:05)
Revealing mistake: In the Torchwood building, a large group of Cybermen start shooting at the Daleks and the Genesis Ark. The Daleks shoot several of them, and you can see a Cyberman that, thanks to hilarious CGI, just collapses like a sock without any physical regard that he is wearing tough metal leg armour, is floating a little off the ground, and falls way too fast than physical laws could allow. (00:25:15)
Continuity mistake: When Rose is hanging onto the lever and beginning to lose her grip, in close-ups of her face her body is facing the other wall of the room, perpendicular to the floor. In shots showing her and her hands on the lever, her body and head are facing the floor. (00:35:55)
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 the two Cybermen meet the Dalek for the first time, they are exterminated. They fall directly in front of the Dalek, but when the camera angle changes to show the second Cyberman hitting the floor side on, you can see the Dalek in the background. The Cybermen both fell straight forward, so it shouldn't have been possible to see the Dalek when seeing the Cyberman side on in the next shot, as the Dalek is facing them both directly.