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)
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.
Other mistake: The Cyber Leader is supposed to follow the Master's footsteps exactly in order to get across the chessboard. He doesn't. This cannot be classed as a character mistake because the Cyber Leader knew what was involved. I believe this mistake was caused by the actor not being able to see the chessboard through his helmet.
Continuity mistake: In episode 1, when the Doctor opens the garage doors with his 'door handle', note the two men in the background, the position of the car behind him and the white pillar. In the next shot, the men and pillar disappear and the car moves to a different spot. In the shot after that, the tanker truck is now parked in front of a pillar. You can see near the beginning of episode 3 that there are two entirely different buildings that the tanker had been filmed in front of. (00:14:25)
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: When Stotz cuts a hole in his ship's door, you can see that the inside of it is made of white polystyrene. They painted the outside of it but obviously forgot about the inside. Also listen to the sound it makes when Stotz punches the hole through - it sounds exactly like polystyrene.
Factual error: Sharaz Jek's monitor that displays the tunnels and his androids is inaccurate. The white blobs are, as we learn later, supposed to represent his androids. He tells the Doctor that the green area is held by the army, yet on the screen the green area is populated by androids, so they could not have had control.