i) births and deaths
31 July 1999: death of Ric Felgate, who appeared in three stories all directed by his brother-in-law Michael Ferguson. He was Roy Stone, an American journalist in The War Machines (First Doctor, 1966), Brent, killed by the Ice Warriors in The Seeds of Death (1969) and astronaut Charles Van Lyden, the first person seen on screen in The Ambassadors of Death (Third Doctor, 1970).
31 July 2000: death of Roy Purcell, Chief Prison Officer Powers in The Mind of Evil (Third Doctor, 1971) and President of the Council of the Time Lords in The Three Doctors (Third Doctor, 1972-73)
31 July 2004: death of Robert James, who played gullible scientist Lesterson in The Power of the Daleks (Second Doctor, 1966) and the High Priest in The Masque of Mandragora (Fourth Doctor, 1976)
ii) broadcast anniversaries
iii) date almost specified in canon
31 July 1977: the latter part of episode 3 and all of episode 4 of Image of the Fendahl (1977) are set on a day specified as 'Lammas Eve' (the day before 1 August, ie 31 July) by Mrs Tyler. There is no reason to suppose that the year is other than 1977.
31 July 1988: birth of the Eighth Doctor's audio compainion Lucie Miller, played by Sheridan Smith. Do give her plays a listen - the chemistry with McGann is great.