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)
The Impossible Planet (1) - S2-E11
Plot hole: The Doctor and Ida are stranded 10 miles down, and yet the lift travels very slowly, like walking pace. They only have an hour's worth of oxygen left in their suits - by the time they get to the surface, it would have run out.
The Impossible Planet (1) - S2-E11
Plot hole: The rocket flew down a gravity funnel and (presumably) crash-landed on the planet, since the true Captain died during the landing. The rocket is big, but surely not large enough to contain all the 'flat-packed' materials for the sanctuary base (which is massive) and the gantry which supports the rocket. Where did that gantry come from? It is the same size as the rocket. It is not possible that the sanctuary base and rocket gantry could have fitted on board that rocket.
The Impossible Planet (1) - S2-E11
Continuity mistake: After Ida retracts the roof to show the black hole, there is a shot where the Doctor and Rose are looking at it, with nothing above them, as he explains about it. However, other shots of the base's control room show that there are things in the room, such as wires connecting the central computer table to the walls, that should have been visible. (00:08:00)
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.
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)
The Christmas Invasion - S2-E2
Other mistake: When Rose and Mickey are running across the plaza after being dropped off by a cab, a fence is visible between where they are and where the cab pulled up. It is unlikely to say the least that they would have gotten out of their cab right by a fence and climbed over it. (00:08:45)
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)
Factual error: The Olympic torch relay is presented as if there is only one runner carrying the torch through the entire city of London to the Olympic stadium to light the cauldron. Furthermore, when the torchbearer collapses, the TV announcer reacts as if it is now impossible to get the torch to the stadium, just before the Doctor steps in and picks it up. Any broadcast of any Olympic opening ceremonies would show that that's not how the torch relay has ever worked.
