The decision to have the Doctor impersonate his previous incarnations was made during rehearsal when Peter Davison presented impersonations as part of his preparation for taking on the role; his interpretation was intended to combine elements of the past Doctors.
Elisabeth Sladen (Sarah Jane Smith) and Louise Jameson (Leela) were each asked to reprise their companion roles in order to ease an audience, many of whom had only ever known Tom Baker in the character, into a new Doctor. Each of the actresses declined.
The fact that the Fifth Doctor is not wearing the same shoes as those his predecessor is not without precedent in the history of regeneration stories. The Second Doctor appeared to have "regenerated" items of clothing along with his body when he emerged in The Power of the Daleks: Episode One (1966). There is no scene in that story where the Second Doctor changes clothes; the First Doctor's clothes have ostensibly regenerated with him. Likewise, the Fourth Doctor has different shoes and a different jacket from the Third's Spearhead from Space kit. The difference here is that the production team admitted to simply making a continuity error; they were not deliberately trying to imply - as arguably Innes Lloyd's team were - that the clothes regenerated with the man.
This is the first story to have the Doctor credited as "The Doctor" (rather than previously as "Doctor Who" or simply "Dr. Who").
This was the first-ever Doctor Who (1963) episode to include a pre-credits sequence, though it is simply a recap of the last scene from the previous season as the show had been off the air for almost a year.