6 December 1932: birth of Declan Mulholland, one of the few Northern Irish actors to appear in Who, as Clark in The Sea Devils (1972) and Till in The Androids of Tara (1978).
6 December 1975: birth of Noel Clarke, who played Mickey Smith in New Who (2005-2009)
ii) broadcast anniversaries
6 December 1975: broadcast of third episode of The Android Invasion. The Doctor learns the Kraal's plan; Sarah saves him from brainwiping; and they both stow away on the rocket to Earth.
6 December 1980: broadcast of third episode of State of Decay. Tarak rescues the Doctor and Romana, but is killed by the vampires.
6 December 1986: broadcast of second episode of The Ultimate Foe (ToaTL #14), ending Season 23. Last appearance of Colin Baker as the Doctor. The Doctor escapes the Matrix and thwarts the Master and the Valeyard. But I'd stay off the exercise bike if I were you, Doctor.
6 December 1989: broadcast of third episode of Survival, the final episode of Season 26 and indeed the very last episode of Old Who, so also the final appearances of Sylvester McCoy as the Doctor, Sophie Aldred as Ace and Anthony Ainley as the Master. (See 20 August for an interesting coincidence linking those three.) The Master tries to take over the youth club in Perivale, but the Doctor lures him back to the cheetah planet and leaves him there, walking off into the sunset with Ace.
[I hadn't realised the coincidence that the last Sixth Doctor episode was broadcast exactly three years before the last Seventh Doctor episode.)
iii) date specified in canon
6 December 1963: burial of British Army sergeant Mike Smith (as seen in Remembrance of the Daleks in 1988).