The Doctor's farewell speech to Mel was the audition speech that Sylvester McCoy was given when trying out for the role, and when it became clear that this was going to be Mel's last episode he insisted that they use that.
The scene where Kane deliberately opens a screen to melt was inspired by Count Orlok's death in Nosferatu (1922).
Kane's death scene was filmed using a wax bust of the actor's face, which was melted down in front of a recording camera, with the footage later sped up for incorporation in the episode. In the scene where Kane's bust melts, there is a notable absence of red wax to tone his demise down for a family audience.
This was the first televised story since The Invasion of Time: Part Six (1978) where a companion left the Doctor at the end of a season, and the first story since that same serial where one joined the Doctor in a season finale, apart from Tegan Jovanka (Janet Fielding) who joined the Doctor in "Logopolis," the final story of Season Eighteen.