Romana's regeneration establishes that a Time Lord can regenerate into the form of someone that they previously met. This would later occur when the Fifth Doctor regenerated into the Sixth Doctor, played by Colin Baker who had previously played Time Lord Security Commander Maxil in the serial Arc of Infinity: Part One (1983). It would also become an important theme for the Twelfth Doctor, played by Peter Capaldi.
Douglas Adams added the scene in which the Doctor humorously taunts the Daleks about their inability to follow him up a vertical shaft. Terry Nation disliked this, as he believed that pointing out the Daleks' apparent design flaws made them less menacing, and threatened their popularity with the viewing public.
The author of the book read by the Doctor, "The Origins of the Universe", is Oolon Coluphid. According to script editor Douglas Adams' "The Hitchhiker's Guide to the Galaxy", Oolon Coluphid is the author of the trilogy of philosophical blockbusters "Where God Went Wrong", "Some More of God's Greatest Mistakes", and "Who Is This God Person Anyway?".
This was the last Doctor Who (1963) serial to be written by Terry Nation. However, according to director Ken Grieve, script editor Douglas Adams wrote 98% of the serial (for which he was uncredited).
Another reason why K9 was left in the TARDIS was that Terry Nation disliked him and didn't want him to face the Daleks.