100,000 BC - S1-E1
Character mistake: When Ian is trying to escape from the TARDIS in episode 1, he says, "He closed the door from over there, I saw him." It was in fact Susan who closed the door.
Character mistake: A Sensorite says, "Give my Doctor the congratulations," instead of "Give the Doctor my congratulations," in the fourth episode.
Visible crew/equipment: (Ep. 2) When The Doctor, Jo, and Dr. Tyler are taken into Omega's palace, in the first shot of the multiple passageways (right before Jo says that it looks like Aladdin's cave) the curved chalk actor's mark is visible on the floor, then we see it again in three following shots. Note that when they're all escorted further inside, just as Dr. Tyler comments about the matter/anti-matter not making sense, Jon Pertwee looks down, presumably to make sure he hits his mark.
The Doctor: This is a situation that requires tact and finesse. Fortunately, I am blessed with both.
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