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42 - S3-E7

Character mistake: The question to unlock one of the doors asks for the next number in the sequence 313, 331, 367. The Doctor gives the answer as 379 with a convoluted (albeit correct) explanation of happy primes, but there are much simpler solutions. The difference between the first and second numbers is 18 and the difference between the second and third is 36 (which is 2 x 18), suggesting that the difference between the third number and the next could be either 54 (= 3 x 18), giving 421 as the next number, or 72 (= 2 x 36), giving 439. It's likely that the Doctor would see that the answer is ambiguous, and yet he confidently states that the most complicated answer is correct. (00:08:45 - 00:09:15)

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Army of Ghosts (1) - S2-E15

Character mistake: Dr Singh refers to "a single protozoa." "Protozoa" is the plural form. He ought to have said "a single protozoan." (00:08:05)

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The Idiot's Lantern - S2-E10

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)

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World War Three (2) - S1-E5

Character mistake: The Doctor comments that the destruction of Earth will cost 5 billion lives. At the time of the episode (2006, one year on from when Rose met the Doctor), the population of Earth was around 6.5 billion. (00:25:10)

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Samsara - S11-E2

Character mistake: Rimmer says the odds of throwing a 1 and a 2 are 18 to 1. The probability is 1 in 18, but the odds are 17 to 1.

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Character mistake: Spanish headlines are seen. Some of the a's have the wrong accent on them ("å" instead of "á"). (00:45:25)

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Episode 8 - Season 2 - S2-E8

Character mistake: Sue White suggests speaking in Portuguese but what she says next is actually Spanish. (The subtitles incorrectly say she is speaking Portuguese). (00:04:00)

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Episode #9.3 - S9-E3

Character mistake: Tariq says "I ran a probability logarithm." This makes no sense: it should be "a probability algorithm." (00:17:35)

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Character mistake: The doctor diagnosing Will's illness tells Evelyn and Max that it's caused by "an isotope called polonium." Polonium is a chemical element, not an isotope. The word "isotope" refers to a form of an element (such as carbon-12 or carbon-14) not the element itself. It does not mean "radioactive substance", because many isotopes are stable. A doctor would know this. (00:17:00)

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Sabotage - S1-E6

Character mistake: In the epilogue, Charlie illustrates the relationship of mathematics to real life by discussing the golden ratio and its presence in a host of real-life situations, including the shape of a nautilus shell and the distribution of petals in a flower. These claims are disputed by some mathematicians (see http://en.wikipedia.org/wiki/Golden_ratio#Nature), and the one about the nautilus shell one is untrue (see http://en.wikipedia.org/wiki/Golden_spiral#Spirals_in_nature). It's possible Charlie is just repeating what he has read or heard without investigating it for himself, but this is uncharacteristic of him.

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Character mistake: Sauvage declares that he is going to turn England into a prison, but the graphic he is displaying puts the prison walls around the entire island of Great Britain. (01:03:30)

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Episode #4.4 - S4-E4

Character mistake: A computer screen giving details of the villain of the week contains various spelling and grammatical errors: "Embassey", "Assination" and "Assination of with".

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Episode #4.1 - S4-E1

Character mistake: Ruth requests a search of London streets with the name "Achilles" in them. A list of streets appears on a computer screen, but when one of them is selected, it is spelled "Achillies."

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Army of Ghosts (1) - S2-E15

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.

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