Late and brief, I'm afraid...
The Unquiet Dead: This is basically the source story here. Doctor shows off by taking companion to requested historical destination (only he gets the time and place slightly wrong); said destination is being invaded by homeless aliens who have designs on Earth, Doctor and companion vow to go as far as sacrificing their lives to stop them, moralising about who one can/can't save. Girls with second sight making prophecies of visible relevance to the rest of the season. The Doctor even technically meets literary figures, in the form of the Caecillii. At the end of the episode he officially confirms Donna as companion.
Boom Town: Just as Margaret Slitheen predicted, the Doctor saves one family, and assuages his conscience.
Rise of the Cybermen/The Age of Steel: Baddies plan to convert the whole human race to become like them, and take over the world.
The Satan Pit: Underground Balrog-like monster that gets loose; it's already been working its influence on some of the population, and they're physically marked by this.
The Shakespeare Code: Historical done as comedy, with anachronistic gags ("T.K. Maximus," etc.) Also (and this goes for "The Unquiet Dead," "The Idiot's Lantern, etc.), the idea that one can't do a straight historical, there has to be a monster in it somewhere.
Gridlock: Doctor bonds with companion at end of story over the nature of his life as a time lord; major prophetic revelations given in cryptic manner.
Daleks in Manhattan: Wales as stand-in for more glamourous location; some of the team go to said glamorous one and don't let anyone forget it.
Catchprasewatch: Looks like this "everyone assumes they're married" gag is going to become a recurring thing. "Allons-y, Alonzo," and a blink-and-you-miss-it "bwilliant".
Old Skool Who: The Aztecs, the Massacre, and The Reign of Terror get the whole "can you or can't you change history?" question resolved at a stroke (answer: sometimes), while The Romans is actually namechecked and The Myth Makers is also a visible influence. Any story in which a cult attempt to sacrifice the Doctor and/or companion; take two points if their reasons are actually other than religious (The Masque of Mandragora, Meglos, and see elsewhere); The Brain of Morbius (The Sisterhood called, they want their robes, makeup, and chanting-and-whirling schtick back). Big Finish did a CD called "The Fires of Vulcan" focusing around Pompeii.
Everything Else: The Confidential admits to Asterix and the Cambridge Latin Course (though IIRC the Caecillii never had a daughter), but other candidates include the HBO/BBC series Rome and, indirectly, I Claudius (Ancient Romans talking and acting like modern people), The Terminator ("Take my hand [if you want to live]"), Spartacus ("I am... Spartacus." "I'm Spartacus too"). A short-lived 1980s transforming toys franchise called "Rock Lords" (it was basically Transformers with rocks, and the creatures looked a lot like those Pyrovile things). Actual Pompeian history/archaeology (people turning into stone is a creepy reference to the petrified casts of Pompeians buried under the ash). Only Fools and Horses ("lovely jubbly"). Up Pompeii is going to be an unconscious influence regardless of what you do. That Star Trek episode where the crew journey back to the 1960s and accidentally kidnap an astronaut (in that the question of what to do with him is influenced by the question of how historically significant he and his offspring will be, much like the Doctor with the Caecillii).