4 October 1922: birth of Dudley Simpson, composer extraordinaire. Here's the Fourth Doctor's theme.
4 October 1987: birth of Daniel Anthony, who played Clyde Langer in the Sarah Jane Adventures.
ii) broadcast anniversaries
4 October 1975: broadcast of second episode of Planet of Evil. The Doctor finds the pool which is the interface between the universes of matter and anti-matter; and falls into it.
4 October 1976: broadcast of a Doctor Who segment of the children's radio programme Exploration Earth, starring Tom Baker as the Doctor and Elisabeth Sladen as Sarah Jane Smith exploring the geological history of Earth and defeating the Megron.
4 October 1980: broadcast of second episode of Meglos. The cactus now looks like the Doctor and steals the mystic Dodecahedron.
4 October 1986: broadcast of first episode of Mindwarp (ToaTL #5). On Thoros Beta, the Doctor and Peri encounter their old enemy Sil and the shouty shouty King Yrcanos. Yet again, the Doctor's brain is under threat.
4 October 1989: broadcast of first episode of Ghost Light. The Doctor brings Ace to the house known as Gabriel Chase, several decades before she burns it down. Its inhabitants are very strange.
4 October 2011: broacast of second part of Sky (Sarah Jane Adventures).
4 October 2014: broadcast of Kill the Moon.
iii) date specified in-universe
4 October 1999: Birth of Jack Harkness's grandson, Steven Carter