12 January 1974: broadcast of first episode of Invasion of the Dinosaurs, billed simply as Invasion. The Doctor and Sarah land in a deserted London under martial law, and are attacked by first a pterodactyl and then a tyrannosaurus rex.
12 January 1980: broadcast of fourth episode of The Horns of Nimon, ending Season 17 prematurely. K9 rescues the hostages and the Doctor and Romana blow up the Nimons' complex.
12 January 1982: broadcast of fourth episode of Castrovalva. The Portreeve turns out to be the Master, and the whole of Castrovalva based on Adric's computations. The Doctor rescues Adric and leaves Castrovalva to fold in on itself, trapping the Master.
12 January 1983: broadcast of fourth episode of Arc of Infinity. Omega attempts to transfer across to our universe, but the Doctor prevents him; and Tegan rejoins the Tardis.
12 January 1984: broadcast of third episode of Warriors of the Deep. The Doctor kills the Myrka, but the Sea Devils take over the base.
Also 12 January 1984: filming of the regeneration scene from the Fifth Doctor to the Sixth.
12 January 1985: broadcast of second episode of Attack of the Cybermen. The Doctor helps the Cryons attack the Cybermen, and Lytton, dying, kills the Cyber-Controller.
12 January 2020: broadcast of Orphan 55. Not everything is as it seems at Tranquility Spa — why is the staff so worried about oxygen levels? What are the monsters stalking the corridors? And why does the planet on which they're all standing bear the ominous name of "Orphan 55"?
ii) date specified in canon
12 January 1898: death of Florence Sundvik (in The Curse of Fenric, Seventh Doctor, 1989)