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.
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)
Continuity mistake: Rita has her right arm up in front of her while her husband is shouting at her. She lowers her arm, and in the next shot, she is holding it up again. (00:10:10)
Continuity mistake: When the Doctor is in the cage with the faceless people, his flashlight switches from his left hand to his right hand and back. (00:18:25)

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. (00:38:25)
Factual error: One of the programs on the new television set is Animal, Vegetable, Mineral? In 1953, this quiz show was broadcast on Thursdays. But, it's the eve of the coronation, which makes it Monday the 1st of June. Animal, Vegetable, Mineral? wasn't on that evening.
Continuity mistake: When the Doctor first gets on his scooter, we see Rose putting her helmet on before she gets on, but she doesn't do her chin strap up. When we next see her, on the bike, her strap is done up.
The Impossible Planet (1) - S2-E11
Continuity mistake: When Rose, the Doctor, and the others are running across the walkway a stream of steam appears and disappears between shots. (00:03:55)
The Impossible Planet (1) - S2-E11
Factual error: The Doctor (and the staff on the station) refer to the idea of a planet being in orbit around a black hole as 'impossible'. It is not. Gravity (and physics in general) works perfectly well outside of the event horizon. For all practical purposes - regarding orbiting around it - the black hole might as well be any other object, as long as it has an equal mass. (00:07:15 - 00:08:30)