16 January 1979: death of Peter Butterworth, who played the Meddling Monk in The Time Meddler (1965) and The Daleks' Master Plan (1966).
ii) broadcast anniversaries
16 January 1965: broadcast of "The Slave Traders", the first episode of the story we now call The Romans. The Tardis crew are relaxing in a Roman villa. The Doctor and Vicki decide to walk to Rome, and the Doctor takes on the identity of a murdered musician. Barbara and Ian are captured by slavers.
16 January 1971: broadcast of third episode of Terror of the Autons. Plastic daffodils are programmed to asphyxiate people all over Britain, and the Doctor is attacked by his telephone cable.
16 January 2008: broadcast of Kiss Kiss Bang Bang, starting the second season of Torchwood. This is the one with James Marsters appearing as Captain John Hart; the team prevent him from destroying Cardiff and he disappears remarking that he has 'found Gray'.
iii) date specified in canon
16 January 2197: The Sixth Doctor and Evelyn Smythe materialise on the spaceship Valiant, as recounted in Nicholas Briggs' 2006 Big Finish audio The Nowhere Place.