Although the Cybermen refer to the events of "Tomb of the Cybermen" (1967) during the flashback sequence, the story was not extant in the archives at the time, so a clip from The Wheel in Space: Episode 6 (1968) was used instead.
Despite being the main guest star of this serial, Beryl Reid's screen time in parts 2 to 4 amounts only to 20 minutes.
The reason for the Third Doctor's omission from the flashback clips was that he never encountered the Cybermen during his original tenure. In relation to this story, the Cybermen's encounter with the Sixth Doctor, (Attack of the Cybermen) in 1985 would have also been part of their chronological past as would be their 1988 encounter with the Seventh Doctor in Silver Nemesis. Neither were seen as part of the flashback clips. The real world reason for this, of course, was that although these events would have happened already in the timeline, these serials (with their respective Doctors) had not yet been created for the show.
Beryl Reid was cast by John Nathan-Turner because she was a big name. The rest of the cast was chosen by Peter Grimwade. The regular cast and writer Eric Saward thought Beryl Reid was miscast. According to Peter Davison, she didn't understand the story at all.