Corrected entry: At the climax, the Doctor and Morbius engage in a mental duel. When the Doctor appears to be losing, the faces of the First Doctor appears, followed by several other adult male faces in various period clothing. The suggestion appears to be that these are previous incarnations of the Doctor prior to William Hartnell's version. Indeed, this was the idea at the time the story was broadcast (the faces themselves were those of various production members). However, if the William Hartnell incarnation was not the first Doctor Who, but the fourth (at least) that goes against the entire continuity of every Doctor Who story..
Doctor Who (1963)
1 corrected entry in season 13
Other mistake: 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.
The Doctor: This is a situation that requires tact and finesse. Fortunately, I am blessed with both.
Trivia: Such was the popularity of Doctor Who in Britain in the mid-1960s that even the Beatles wanted to make an appearance in the show. So a scene was written into "The Chase" to allow them to appear. The idea had been devised of including a scene on the Time and Space Visualiser depicting a Beatles fiftieth-anniversary concert in 2015, with the Fab Four dressed up as old men. John, Paul, George, and Ringo themselves were interested in the proposition, but it was vetoed by their manager, Brian Epstein. It was then thought that an appearance by the Beatles on Top of the Pops might be used instead, but no such footage was available. Fortunately, the Beatles were scheduled to perform "Ticket to Ride" at Riverside Studios in Hammersmith on April 10th, 1965, and that footage was used instead.
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?
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.
Correction: There are unknown faces shown, but Morbius was a Time Lord, too; they are HIS past incarnations.