Continuity mistake: During the animated portions of Shada's missing scenes, in numerous shots an illustrated character's clothing (buttons, scarf, etc) become flipped, sometimes even within the same shot. Example: when The Doctor goes to the physics lab and meets Clare Keightley, note her buttons and The Doctor's scarf.
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)
Revealing mistake: Susan is supposed to be running through a forest. It is painfully obvious that, in fact, she is simply running on the spot against a back-projected film, and the branches that hit her are simply studio stagehands, hiding just out of shot, hitting the actress with twigs.
Plot hole: Yartek tried to disguise himself as Arbitan by wearing Arbitan's robes and pulling the hood over his giant rubber head. Strangely enough, no-one seems to notice that "Arbitan" is now suddenly speaking with a completely different voice, and now has a two-foot-tall-head.
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.
Continuity mistake: The caption slide at the end of episode two reads: 'Next Episode: The Cave of Five Hundred Eyes'. While the title slide comes up at the start of episode 3, it simply says "Five Hundred Eyes".
Other mistake: William has a bit of a nightmare, completely throwing the others during one scene by saying the same line ("It's not very likely") twice, and fumbling the line "You knocked both Susan and I unconscious". He also omits the scripted explanation for the melted clocks.