Trivia: David Troughton, who plays King Peladon, is the son of the Second Doctor, Patrick Troughton. Both Troughtons had previously appeared together in the Season 6 (1969) story 'The War Games'; Patrick Troughton as the Doctor, and David Troughton in the minor part of a soldier called Private Moor. Additional trivia point: David Troughton shared a flat with future (Sixth) Doctor Colin Baker at the time of the making of 'The Curse of Peladon' (January 1972).
Trivia: This Doctor Who story, first broadcast between April 8th and May 13th 1972, is called "The Mutants." However, the second ever Doctor Who story, first broadcast December 21st 1963 to February 1st 1964, was also known as "The Mutants." Looks as though no-one bothered to check if the title had already been used... of course, since that serial later came to be called "The Daleks", that likely explains it.