Plot hole: Peri goes to a fair bit of trouble to bolt the door on the bath house when rescuing the Doctor. When the Rani and the Master arrive, they simply open the door. Now this, in itself, isn't a mistake, as the Master has a special gadget for opening locked/bolted doors, but both the Master and the Rani seem surprised that someone is in the bath house.

Doctor Who (1963)
1 plot hole in The Mark of the Rani - chronological order
Planet of the Spiders - S11-E5
Plot hole: At the climax of episode 2, the Doctor is about to catch Lupton when the latter simply teleports to safety. So why didn't he do that in the first place, before engaging in a 15-minute chase?
The Doctor: This is a situation that requires tact and finesse. Fortunately, I am blessed with both.
Trivia: This Doctor Who story was originally scripted and produced as a four-episode story, but, just two weeks before transmission, upon viewing the story, co-creators Sydney Newman and Donald Wilson felt that the final two episodes (Episode 3, 'Crisis'; and Episode 4, 'The Urge to Live') should be combined into a single episode. The new 'condensed' episode incorporated the opening titles of 'Crisis' with the closing credits of 'The Urge to Live'.
Earthshock - S19-E6
Question: In Earthshock, season 19, at the end of episode 3, the Cyber Leader views his troops marching down the corridor. Each column is headed by a Cyber Leader. Is this a mistake, or is there more than one Cyber Leader allowed per army?
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Answer: In 'The Five Doctors', three separate Cyberleaders are definitely used. So it's likely that Cyberleaders are like unit commanders, of which a fair-sized army might have several.
Daria Sigma