6 May 1945: birth of Nicholas Mallett, who directed The Mysterious Planet (Sixth Doctor, 1986), Paradise Towers (Seventh Doctor, 1987) and The Curse of Fenric (Seventh Doctor, 1989)
6 May 1976: death of Alethea Charlton who played Hur in An Unearthly Child (First Doctor, 1963) and Edith in The Time Meddler (First Doctor, 1965). Here she is from the same angle in both stories.
ii) broadcast anniversaries
6 May 1967: broadcast of fifth epside of The Faceless Ones. The Chameleons explain that they lost their identities. In an explosion.
6 May 1972: broadcast of fifth episode of The Mutants. The Marshal forces the Doctor to work for him by holding Jo hostage.
6 May 2006: broadcast of The Girl in the Fireplace. The Doctor, Rose and Mickey land on a far future spaceship and the Doctor become involved with Madame de Pompadour.
6 May 2017: broadcast of Kock Kock. Bill and her friends rent an old house to live in, but the floorboards and the walls are creaking, and there's a creepy Landlord lurking around. Can the Doctor save the day as creatures come crawling out of the wood?
6 May 2020: webcast of Pompadour, a creepy take on The Girl in the Fireplace.
iii) date specified in canon
6 May 1997: setting of Lance Parkin's Virgin New Adventure The Dying Days, featuring the Eighth Doctor and Bernice Summerfield.