Factual error: The story The War Machines is (probably) set in London in July 1966. At the time, England, and more specifically, London, was hosting the FIFA World Cup Soccer Tournament. Yet, you wouldn't know it from watching this Doctor Who story...Sir Charles Summers mentions July 12th (1966) which was the day after England played Uruguay at Wembley and the day before Mexico played France. The other matches involving those four were played in London during the time the events of The War Machines are supposed to take place, yet no mention is made of the fact, there are no foreign football supporters roaming the streets and no flags or posters on display. Did the story take place in an "alternate reality" London of July 1966?
Factual error: In 1638, a mathematician calculates that the asteroid will return in 350 years time, on the 23rd of November 1988. But in 1752, Britain's calendar was moved forward 11 days so that it matched with that of the Vatican. This means the asteroid would return on 4th December, so everything that is supposed to happen in this story after 1752 is 11 days out.
Deliberate mistake: Look for the "creases" in the wall inside the TARDIS, which look as if the wall was just a sheet hung up behind the console.(In fact it actually WAS a sheet and not a "solid" wall the TARDIS wall prop was apparently unusable due to water damage, due to poor storage between seasons. This also explains the lack of TARDIS interior scenes throughout the rest of season 26: it was not thought worth repairing the TARDIS set (or building a new one) when the show was in imminent danger of being cancelled after season 26.).
Revealing mistake: In the UNIT tracking room, there is a flimsy railing behind the radar operators that Chinn knocks as Yates leads him off to the "direct" phone line, causing it to wobble badly. The Doctor then deals the railing another blow as he comes up to look at the console.
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Factual error: Sharaz Jek's monitor that displays the tunnels and his androids is inaccurate. The white blobs are, as we learn later, supposed to represent his androids. He tells the Doctor that the green area is held by the army, yet on the screen the green area is populated by androids, so they could not have had control.
Revealing mistake: When Stotz cuts a hole in his ship's door, you can see that the inside of it is made of white polystyrene. They painted the outside of it but obviously forgot about the inside. Also listen to the sound it makes when Stotz punches the hole through - it sounds exactly like polystyrene.