21 January 1978: death of Geoffrey Orme, who wrote The Underwater Menace.
21 January 1993: death of David Blake Kelly, who played the captain of the Mary Celeste in The Chase (1965) and Jacob Kewper in The Smugglers (1966)
ii) broadcast anniversaries
21 January 1967: broadcast of second episode of The Underwater Menace. The Doctor causes a power cut and Ara rescues Polly. Zaroff explains that he intends to destroy the Earth.
21 January 1978: broadcast of third episode of Underworld. The Trogs rebel against the Guardians; the Doctor and Leela prepare to infiltrate the Citadel.
(Two particularly duff episodes today, in my opinion.)
iii) date specified in canon
21 January 1941: the Doctor and Rose trace a mauve alert to London and meet Captain Jack Harkness, as see in The Empty Child (2005).