Plot hole: In the middle of chasing the Doctor, Stor abandons the idea of controlling Gallifrey in favour of destroying it for no readily apparent reason.
Plot hole: Leela's decision to stay with Andred is very sudden. They barely speak during the serial.
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.
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: If the Doctor gets a TARDIS, does that mean other Timelords get a TARDIS as well?
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 ★