Plot hole: Those people created for medical experiments cannot run. In fact they can barely walk, so how come they can climb nearly as fast as Rose? What's more, when you see them climbing, they seem to have little ability to coordinate hand over hand. Even with the delay brought on by the cat-woman-thing, they should not have been able to keep up with her.
Character mistake: When the Doctor and Rose are walking back to the TARDIS at the end, he explains to her that Queen Victoria was hemophiliac. She wasn't. She was a carrier of the disease due to a mutation in one of her parents' reproductive cells (probably her father, Edward, Duke of Kent, because he was in his fifties when Victoria was born), but since she only had it in one of her X chromosomes, she didn't actually suffer from it as the gene for it is recessive, which is why most hemophiliacs are male. It is true that several of her children inherited the gene, and one of her sons was hemophiliac, but not Victoria herself. (00:40:55)
Factual error: The Koh-i-Noor, as depicted in this episode, looks absolutely nothing like the real diamond. The episode's gemstone is about the size of the palm of the Doctor's hand, and shaped in a stereotypical brilliant cut. The real Koh-i-Noor is much smaller and oval-shaped.
Continuity mistake: During the Doctor and Sarah Jane's conversation in the café while he's repairing K9, when Sarah mentions the events of "The Christmas Invasion" and the Doctor confirms that he was there, the Doctor's hold on a piece of wire from K9's insides changes between shots. (00:17:20)
Continuity mistake: During the Doctor and Sarah Jane's conversation in the café, when Sarah says that she missed him and he responds that she was getting on with her life, in a shot facing Sarah, the Doctor's hands are not visible repairing K9. In the next shot, facing him, his left hand is suddenly on the robot, in a position where it should have been visible in the preceding shot. (00:17:45)
Continuity mistake: When Mickey pulls the blanket off K9 and turns him on to ask if he has anything to get them inside the locked school, K9's right side panel is missing, exposing the wires and circuitry inside him. When he turns up in the cafeteria to help the others escape the Krillitanes, the missing panel has suddenly appeared. (00:34:10)
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. (00:36:25)
Continuity mistake: When Sarah Jane breaks into the school, she has her purse with her. However, after she runs out of the hall with the headmaster's office after hearing some unsettling noises, it disappears, as she no longer has it when she finds the TARDIS hidden in a storage room off the gym.
Continuity mistake: For most of the scene where he's probing Reinette's mind to find out what the clockwork droids want with her, placing his hands on her temples, the Doctor's left hand is positioned with two fingers on either side of her ear. When he realises that she's seeing some of his memories, his ring finger has jumped to being in front of her ear, without him taking his hands from her head. (00:20:50)
Other mistake: When the Doctor finds the crystal and blows on it, it glows brightly. While it lights up his face as it should, the backs of his hands light up, apparently from the crystal. This is not possible, as the light comes from in front when the crystal is inside the Doctor's hands. (00:14:55)