i) births and deaths

28 May 1935: birth of Anne Reid, who played Nurse Crane in The Curse of Fenric (1989) and Florence Finnegan in Smith and Jones (2007)

28 May 1940: birth of Frank Cox, who directed part 2 of the story we now call The Edge of Destruction (First Doctor, 1964) and parts 5 and 6 of the story we now call The Sensorites (also First Doctor, 1964).

28 May 1966: birth of Sharon D. Clarke, who played Graham’s wife and Ryan’s grandmother Grace in Series 11 and 12 of New Who (2018, 2020).

28 May 1968: birth of Kylie Minogue, who played Astrid in Voyage of the Damned (Tenth Doctor, 2007).

(Births also of Patricia Quinn and Faith Brown in 1944, Michelle Collins in 1963 and Carey Mulligan in 1985; much as I enjoyed their appearances in Who, they don't fit my criteria for a full mention.)

ii) broadcast anniversaries

28 May 1966: broadcast of first episode of The Savages, the first episode not to have an individual title. The Doctor, Steven and Dodo are welcomed by the Elders, but something very sinister is going on with their savage neighbours…

28 May 2005: broadcast of The Doctor Dances. The Doctor realises that the gas mask zombies are being created by escaped medical nanocytes, and set matters aright.

28 May 2011: broadcast of The Almost People. The Doctor and the Gangers, and a major plot twist involving Amy at the end.