15 April 1921: birth of David Garth, who played Solicitor Grey in The Highlanders (Second Doctor, 1967-68) and a Time Lord messenger in Terror of the Autons (Third Doctor, 1971)
15 April 1922: birth of Peter Moffatt, who directed State of Decay (Fourth Doctor, 1980), The Visitation (Fifth Doctor, 1982), Mawdryn Undead (Fifth Doctor, 1983), The Five Doctors (Fifth Doctor and friends, 1983), The Twin Dilemma (Sixth Doctor, 1984) and The Two Doctors (Sixth Doctor and friends, 1985). Has any other director directed stories with six different Doctors in them?
15 April 1997: birth of Maisie Williams, who played the recurring character Ashildr/Me in several 2015 stories.
ii) broadcast anniversaries
15 April 1967: broadcast of second episode of The Faceless Ones. Polly and Ben have disappeared; Jamie meets Samantha Briggs; the Doctor is knocked out by gas.
15 April 1972: broadcast of second episode of The Mutants. The Marshall forces the Doctor to work with Jaeger, while Jo is a captive of the Solonians.
15 April 2006: broadcast of New Earth, starting Series 2 of New Who. The Doctor and Rose visit a far-future hospital where they encounter some former acquaintances.
15 April 2017: broadcast of The Pilot, starting Season 10 of New Who, introducing Bill and bringing in Nardole as a regular character. (I remember a fantastic group watch of the episode at Eastercon). The Twelfth Doctor — now living and teaching at St Luke's University on Earth — convinces dinner lady Bill Potts to be his private student. The Time Lord and his companion Nardole soon discover that their new friend has unwittingly made a deal with a prospective girlfriend that threatens their safety in a way that even the TARDIS can't outrun.
(Also NB an earlier Bill and Heather:)
iii) dates specified in canon
15 April 1912: the Titanic, struck by an iceberg late the previous evening, sinks in the early hours of the morning in the North Atlantic with over 1500 lives lost, as seen in the 1979 DWM comic strip Follow that TARDIS!, Kate Orman's 1993 novel The Left-Handed Hummingbird and the 2010 Big Finish audio Wreck of the Titan, also referenced in The Invasion of Time (1978), Rose (2005), The End of the World (2005) and Voyage of the Damned (2007).
15 April 1912: birth date of Charlotte Pollard, companion of the Eighth and Sixth Doctors in many Big Finish audios.
15 April 1980: birth of Samantha Jones, companion of the Eighth Doctor in many BBC-published novels.