The Moonbase - S4-E6
Audio problem: If you listen carefully to the soundtrack of part four of "The Moonbase", some 'chatter' and 'feedback' from the floor manager's headphones can be heard. (At the time this particular episode was recorded, there was just a one-week gap between recording Doctor Who and transmission, so there was no time available to re-record the episode, and this mistake had to be left in).
Factual error: During every outdoor scene in Antarctica, heavy blizzards are shown raging constantly. In reality, such blizzards are extremely rare at the South Pole, thanks to the almost total absence of precipitation Antarctica is effectively a desert, as the air is very dry: with very little moisture in the air, rain or snow is almost impossible.
Continuity mistake: The rhyme the Doctor recites in episode 3 is different from the original rhyme heard in episode 1. (Apparently, the Doctor [William Hartnell] forgot his lines in episode 3, when he came to the point of reciting the rhyme. So he just improvised what he thought they were, rather than what had been scripted).
The Power of the Daleks - S4-E3
Revealing mistake: The Daleks that appear in this and other Doctor Who stories were rather expensive, so some ingenuity was required to make the small number available look like they were more than they were. Tricks employed in "The Power of the Daleks" included making four Daleks look like an army by having them circle around the set a few times (note the delay between the fourth Dalek exiting and the "fifth" Dalek entering), and the blatant use of photographic blow-ups in place of "real" Daleks.
The Moonbase - S4-E6
Revealing mistake: The doors and walls wobble badly as Jamie and Ben barricade the entrance to the medical unit.
Visible crew/equipment: Near the end of episode 3 the inspector is on the plane and just before he goes to look for Captain Blade the camera zooms out and the top of the set is visible.
Continuity mistake: The dialogue between Cutler and the technician at that beginning of episode 3 is slightly from that which closes episode 2.
Continuity mistake: In Episode 1, the TARDIS crew pass out from the change in pressure as they descend into the Earth. However, at the end of episode four, they climb out on foot and suffer no ill effects.
The Evil of the Daleks - S4-E9
Visible crew/equipment: When the Doctor and Jamie enter the secret room watch the top left corner. A boom mike shadow appears and then moves out of shot.
Factual error: In the first close-up view of Mondas, the planet is spinning rapidly so that we can see that its continents are identical to Earth's. But this would mean that Mondas is spinning on its axis once every few seconds - tens of thousand of times faster than Earth. This would be such a fast rotation that the planet would not be able to hold together under the centrifugal force.
Deliberate mistake: The character of "Chicki" is played by a completely different actress in episode 4 to the one who played her in episode 1.
The Power of the Daleks - S4-E3
Deliberate mistake: During all the animated parts of "The Power of the Daleks" in numerous shots various illustrated character's such as The Doctor, Polly, and Ben have their buttons, pockets, patches, etc, flipped to the opposite side, sometimes even within the very same shot.
The Evil of the Daleks - S4-E9
Continuity mistake: (Animated version). Waterfield puts down the photo of the Doctor on his desk but the next time we see his desk the photo is no longer there and then later it's back on the desk again, without Waterfield having moved it.
The Moonbase - S4-E6
Audio problem: In part 4, when the Cybermen are outside The Moonbase controlling the workers, the mouth of the radio operator does not move when he is speaking to them. Furthermore, a few of the Cybermen's mouths outside The Moonbase are stuck open when they have no dialogue.
Factual error: In Episode 3, Zarof fires a gun. The muzzle is seen and a sound is heard but the gun doesn't move and there's no smoke or bullet, no flash or anything at all. (00:23:05)
Answer: It was never destroyed on-screen; it was intact at the end of the TV movie, and destroyed by the start of the 2005 series. It was destroyed in the novel "The Ancestor Cell," but in a completely different manner to what happened in the series.
DaveJB