Remembrance of the Daleks - S25-E1
Factual error: The events depicted are supposed to have taken place at the time of the broadcast of the first Doctor Who story... Saturday 23rd November 1963 at 5:15pm. However, the non-wintry weather and the bright evenings don't fit late November/early December.
Remembrance of the Daleks - S25-E1
Continuity mistake: After the Special Weapons Dalek blows up the gate to Ratcliffe's warehouse, you can see that some of The Daleks were slightly damaged by the explosion. In all the following shots, they have been repaired.
Remembrance of the Daleks - S25-E1
Visible crew/equipment: At the beginning of the episode when the soldier is thrown back after being exterminated, the wire pulling him is very visible.
Remembrance of the Daleks - S25-E1
Character mistake: The gate to I.M. Foreman's scrapyard reads "I.M. Forman."
Remembrance of the Daleks - S25-E1
Continuity mistake: When the Doctor and Ace steal the military van they leave the doors open, but in the next shot when we see the van leaving Totters Lane the doors are suddenly closed.
Remembrance of the Daleks - S25-E1
Other mistake: Right before the Doctor gets attacked by the destroyed Dalek he says: "Let me see, Professor" but the subtitles says: "That's impressive."
Revealing mistake: When Ace and Susan are sitting underneath the huge pipe about to be executed by the Fondant surprise, it's obvious that the actresses aren't sitting directly underneath the pipe, but slightly behind it.
Revealing mistake: In episode one, as the Doctor is repairing the buggy, one of the patrol runs on too soon, realises that he's come in ahead of his 'cue', and runs back.
Audio problem: In episode 2, the Kandyman's microphone picks up quite a bit of the Doctor's dialogue by accident.
Revealing mistake: When the Doctor taps the ice crystals, they wobble instead of breaking.
Plot hole: In episode 1, on both occasions that Silas P presents his card (first to Daphne S, then later to the Doctor), he gives it to his victims the wrong way around. They have to surreptitiously turn it over so that the side with his name on it is facing them, and then act surprised when he tells them to flip the card over to reveal the words "Happiness Patrol Undercover", as if they hadn't seen it before.
Continuity mistake: In the scenes set in the underground tunnels in Part Three, the Kandy Man has no metal brace around his mouth, but he does have the brace in other scenes.
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.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★