The Trial of a Time Lord 9-12 (aka Terror of the Vervoids) - S23-E3
Revealing mistake: In episode 12, while the Vervoids are dying, look out for the ones wearing sneakers and tracksuit pants (complete with drawstrings)...
The Trial of a Time Lord 13-14 (aka The Ultimate Foe) - S23-E4
Revealing mistake: In the final episode, Glitz and the Master leave the console room while the Doctor is driven into submission, but they are quite obviously standing by the scanner screen.
Other mistake: The Brigadier says UNIT HQ is 'a Top Secret establishment'. It is, in fact, so secret that it has a large sign outside informing the world not only of its function, but also the name of the commanding officer.
Castrovalva - S19-E1
The Doctor: That's the trouble with regeneration, you never quite know what you're going to get. (00:12:15)
Planet of the Spiders - S11-E5
Trivia: The first thing the Third Doctor does on-screen is collapse out of the TARDIS, which is also the last thing he does in that incarnation.
Question: In which season and episode is Gallifrey destroyed, or is it just a shocking new plot development for the new series?
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