Revealing mistake: (Part 4) After Omega takes off his mask and looks in the mirror, when he sees that his physical body doesn't exist he puts his mask back on and screams, but when he shouts, "If I exist only by my will, then my will is to destroy," Omega's mask pops up off his face, and we can see the actor's blackened face as he shouts the last bit of his dialogue. (00:07:10)
Plot hole: 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.
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.
Plot hole: After UNIT HQ disappears, you can see a patch of grass where the UNIT HQ used to be...but just exactly how can grass grow underneath a building?
Revealing mistake: When the Doctor and Jo see Bessie in the middle of the rocky area, there is the white chalky substance from the ground on her wheels, indicating she was driven to the spot rather than being "transported" to the black-hole.
Revealing mistake: In episode 3, when the second Doctor, the Brigadier and Benton emerge from the TARDIS, the doors are left completely open with the camera looking straight into them for a long time, revealing not only the emptiness of the police box shell, but also that there's a pair of secret doors on the opposite side to the entrance doors. These 'secret doors' come in handy during episode 4, allowing seven people to come out of the police box in the final confrontation with Omega. (Well, it is stated time and again that the TARDIS is "bigger on the inside than the outside". Now we know how that happens...).
Visible crew/equipment: You can see the reflections of the camera crew in the monitor used to display the First Doctor (William Hartnell). (This is especially noticeable in episodes 2 and 4).
Revealing mistake: At various times (especially in episodes 3 and 4) you can see actor Stephen Thorne's lips through Omega's mask (and in one profile shot you can also see his jaw), yet when his mask is removed, we find that Omega has been dissipated and has no face...
Audio problem: When the companions are returning to Earth via the pillar of smoke, you can see and hear each person walk up the steps and then supposedly disappear. Unfortunately, you can then hear them walk down the other side of the steps..
Continuity mistake: (End of Ep. 3 and start of Ep. 4) When The Third Doctor fights the dark side of Omega's mind, the rings that The Doctor wears on the pinky fingers of both hands switch to his ring fingers, then back again to his pinky fingers, between shots. Then as Omega chokes The Doctor, the ring on his right pinky vanishes between shots.
Audio problem: In Part 3 when the Brigadier gets behind the sand pile with Arthur Ollis, the Brigadier asks him "Did you find a way in?" This is not Nicholas Courtney's voice for this one line. He speaks again right after that and it is his voice. (00:13:20)
Visible crew/equipment: (Part 3) After Omega has revealed himself to The Third Doctor, Jo, and Dr. Tyler, when he begins to speak privately to The Doctor the camera casts a shadow on Omega's body. Then after Omega turns around the boom mic dips into view at the top of the screen. And when Omega starts walking forward, the shadow of equipment (presumably the boom and mic) is moving on the far wall, near the lower left of the screen. (00:03:10)
Visible crew/equipment: When the group are thrown into a dungeon in Omega's palace, you can see tape in the corners which is holding the set together.
Revealing mistake: Whenever the TARDIS's scanner picture of the Doctor's laboratory is shown, the TARDIS itself is always in the picture.
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