16 April 1936: birth of Derrick Sherwin. On paper, he was producer of Doctor Who for only two stories and 14 episodes, the shortest tenure of anyone in the old regime. In fact he was the man who rescued the programme from collapse in Seasons 5 and 6 (as script editor and de facto assistant producer), invented UNIT and the Time Lords, and successfully rebooted the show in colour with a new Doctor in 1970. He also wrote, uncredited, one of the best single episodes of the entire original run, the first part of The Mind Robber
16 April 1954: birth of Antony Root, briefly script editor of Doctor Who in 1981.
16 April 1974: birth of Paul Marc Davis, the only actor to appear in New Who and all three of its spinoffs: as the Futurekind Chieftain in Utopia (Tenth Doctor, 2007), one of the Cowled Figures in Exit Wounds (Torchwood, 2008), the recurring Trickster in the Sarah Jane Adventures, and Corakinus, leader of the Shadowkin in several episodes of Class. His face is only visible in Utopia.
ii) broadcast anniversaries
16 April 1966: broadcast of "The Dancing Floor", third episode of the story we now call The Celestial Toymaker. Steven and Dodo must deal with a not-very-threatening kitchen and some rather more threatening dancing dolls. (I mistakenly used this picture last week.)
16 April 2005: broadcast of Aliens of London. A spacecraft crashes into the Thames; the Doctor is among experts on aliens summoned to 10 Downing Street, but all is not as it seems. Incldues the very first scenes filmed for New Who (with Tosh and the space pig). That same day, the BBC confirmed that David Tennant would play the Tenth Doctor.
iii) date specified in canon
16 April 1746: Battle of Culloden, followed by the events of The Highlanders (Second Doctor, 1966).