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.
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 can be seen on the floor, which can be seen 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 can be seen looking down, presumably to make sure he hits his mark.
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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...).
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...
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.
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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) can be seen moving on the far wall, near the lower left of the screen.