Continuity mistake: When Sarah Jane is talking to Rose while she's trying to access a computer in the lab, half-sitting on the desk, the right side of Sarah's jacket is bunched up beneath her arm in shots facing her and lying down in shots facing Rose.
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.
The Girl in the Fireplace - S2-E7
Factual error: Madame de Pompadour calls herself "Reinette" in 1727, whereas in actual fact, this was a nickname meaning "Little Queen" which was not given to her until 1730. (00:03:45)
The Girl in the Fireplace - S2-E7
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)
The Girl in the Fireplace - S2-E7
Continuity mistake: When Rose is giving the 5 year warning to Reinette, she's got a noticeable spot on her chin. When Reinette goes behind the tapestry and sees the ship, Rose's spot has suddenly vanished. (00:28:50)
The Girl in the Fireplace - S2-E7
Continuity mistake: When the Doctor is trying to fix the connection from the past to the future through the fireplace, the background of the spaceship can be seen behind the flames whilst there is no connection. (00:37:15)
Rise of the Cybermen (1) - S2-E8
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)
Rise of the Cybermen (1) - S2-E8
Continuity mistake: When Rose is sitting on a bench and she gets a news report on her phone, look at the top of the phone screen - it says the time is 11:35. However, several minutes later, when the Doctor and Mickey find Rose, the clock says it's only 11:36. (00:15:05)
Rise of the Cybermen (1) - S2-E8
Visible crew/equipment: Everytime we see a close up of Mickey's grandmother's face, we can see the crew and camera reflected in her glasses. (00:22:20)
Rise of the Cybermen (1) - S2-E8
Other mistake: Alternate Jackie is said to be turning 40. According to a newspaper Mickey finds early in the episode, the parallel universe is in the same year as the main universe. When Jackie's age (she claims to be only turning 39) is announced at the party, Rose does not in any way react as though that's different from the age of main-universe Jackie. The problem is that, given that Rose was 19 when she met the Doctor, and it has been, for main Jackie and Mickey, likely at least two years since the events of "Rose" (remember Rose's one-year accidental disappearance), this means Jackie would have had to have gotten married, and had Rose, before she turned twenty, and been a widow by the time she was twenty. Given that Jackie is from the UK, a first-world country, and that she seems to be in her twenties in "Father's Day", this is highly unlikely.
Suggested correction: "Highly unlikely" is not impossible, there are many cases of this sort of thing happening even in the age of contraceptives. The episode is also set during the 80's, so it's possible that Pete and Jackie were misinformed. There are other TV shows such as Raising Hope or Bump that use this as a major plot point - hell, the very next episode after Fathers Day features an approximately 12-year-old mother in the form of Nancy, the 17-year old mother of antagonist Jamie.
Rise of the Cybermen (1) - S2-E8
Continuity mistake: In this episode's TARDIS scenes, the yellow padded seat is positioned so that it's on the side of the console closer to the door, so people sitting on it are facing away from the door. In all other episodes featuring this version of the console room, the seat is positioned on the side of the console opposite the door.
Continuity mistake: While hiding behind the mini-skips, Rose and Pete hold hands. After a cut to close up, they hold hands again. (00:08:55)
Continuity mistake: When Jake turns on the light in the cabinet with the Cyberman on the zeppelin's bridge, he's holding his handgun in his left hand. The scene cuts away to Mickey briefly, and when it cuts back to Jake his gun has jumped to his right hand. (00:24:30)
Continuity mistake: When the Cyberman is hit by the electromagnetic bomb, it falls to its knees, then backwards. Yet in the next shot, it is flat on its back, with its leg extended. (00:25:20)
Factual error: When Rose gets the message there are two things wrong with what you see on the phones screen: firstly on the top right of the screen you can see the icon for mute even though you heard the beep, and secondly that screen is for when you type in the number you want to call (text), not the screen for receiving a text.
Continuity mistake: Pete Tyler holds the sonic screwdriver against a section of rope next to his leg, but it breaks below his feet.
Suggested correction: After the ladder breaks, and before we see Pete's feet again, we see him climbing a bit up the ladder. When his feet are next shown, he has them on the new bottom rung of the ladder. It would seem that the rope broke exactly where Pete was holding the screwdriver - right by his ankle.
Continuity mistake: When the Doctor and Mrs. Moore are walking through the tunnel of Cybermen, there is constantly a light source in front of them. When the shot looks ahead, there are no lights. This is due to the cameraman giving more light so this all can be filmed.
Visible crew/equipment: When Rose and the Doctor are riding after landing, you see the camera, crew and lighting equipment reflected in their glasses. (00:04:00)
Continuity mistake: When the Connollys are watching TV, in the shots facing the chair and sofa, the chair Eddie was sitting in is further away from the couch than in the shots from above, where the chair is almost touching the couch. (00:04:46)
Character mistake: The Doctor gets excited about the major events of 1953 and mentions that everything was "off the ration" (that is, the food rationing put in place in the UK during the Second World War had ended). Rationing actually ended the following year. (00:05:55)