The Name of the Doctor - S7-E15
Trivia: When Clara jumps into the Doctor's timeline and is shown encountering the Doctor - usually indirectly - in various incarnations and adventures from the classic series, the adventures chosen were mostly ones regarded as being badly written and/or having nonsensical plot elements, with the implication that in-universe, those plot elements were due to the Great Intelligence's meddling. Examples include the notorious instance of the Seventh Doctor dangling himself from a cliff for no reason from the serial "Dragonfire."
The Snowmen - S7-E7
Trivia: The Great Intelligence, the episode's villain, first appeared in a pair of Second Doctor serials, "The Abominable Snowmen" and "The Web of Fear". As a result, there are a few references to the two stories in the episode. First, the Doctor places pieces of the ice governess in a metal lunchbox from the '60s with a map of the London Underground on the lid. He then shows the box to the Intelligence while it is still in the snowglobe, prompting it to ask what the markings mean. The Doctor tells it, and then remarks that the Underground is a "weakness in metropolitan living" because he dislikes tunnels. In "The Web of Fear", the Intelligence and its minions set up in the Underground in the late '60s, with this episode's implication being that, as those events have yet to occur for the Intelligence, the Doctor unwittingly gave it the idea. Second, at the end, the Doctor takes another look at Dr. Simeon's business card for the Great Intelligence Institute and finds the name familiar, but cannot place it, as the Great Intelligence was not actually addressed as such in the episode. When this episode was made and aired, both "The Abominable Snowmen" and "The Web of Fear" were completely lost, with no copies in the BBC archives - a situation that changed less than a year later.
Dinosaurs on a Spaceship - S7-E3
Trivia: Queen Nefertiti's presence, and that she leaves with Riddell in the end, is a reference to the fact that she vanishes from Ancient Egyptian historical records in the fourteenth year of her husband Akhenaten's reign, with no explanation.
Trivia: The amp that the Doctor is using when he's playing his electric guitar at the beginning is from Magpie Electricals, a recurring brand first introduced in Tenth Doctor episode "The Idiot's Lantern". And if you look closely, you'll see the clockwork squirrel mentioned in the previous episode sitting atop it.
Trivia: Steven Moffat was so busy on different projects, and the shooting of Series 6 was enough of a troubled production, that he only had time to write one draft of this episode, which is what was shot. Not only is it amazing that this episode turned out as well as it did given that there was only a first draft of the script, this also explains some problems people have with the episode's plot - problems that probably would have been removed had there been multiple drafts.
Trivia: If you look closely after the Doctor steals the fire truck, a "Vote Saxon" sticker can be seen stuck on the front of the vehicle, most visible in some shots on the highway. This is, of course, a reference to the plot of series 3, when the Master posed as a human using that alias as part of a plan to take over first the Earth and then the universe.
Silence in the Library (1) - S4-E8
Trivia: When this episode and "Forest of the Dead" were made, only Steven Moffat and Alex Kingston knew who River Song really was. As a result, not only is the Doctor's confusion genuine, David Tennant famously admitted that he chose to act as if the Doctor thought that she was a future incarnation of his, even though he knew that, even with what little information was given on River in the story, that theory made no sense.
Trivia: The handles in the escape pod that seal the doors should look familiar - the handle first appeared in "Utopia" as the switch the Master throws to shut down the bunker's defences.
Trivia: Early drafts of this episode had the Carrionite invasion in 1599 (from "The Shakespeare Code") and the Dalek invasion in 1930 (from "Daleks in Manhattan"/"Evolution of the Daleks") stopped by UNIT time-travelling commandos, but this was cut for time and being unnecessary to the main plot.
Trivia: 1999 Comic Relief parody special The Curse of Fatal Death, written by Steven Moffat, managed to accurately predict certain characteristics of several New Series Doctors. The parody Tenth Doctor is quite full of himself and licks a mirror - the canonical Tenth Doctor had a tendency toward confident arrogance that sometimes went drastically wrong, and a noted tendency to lick things. Parody Eleven has several personality similarities to parody Ten, but is noticeably stranger - a description that applies to canon Eleven fairly well. And, last but certainly not least, parody Thirteen being a blonde woman was played for laughs in the special, but the real Thirteen being one was not played that way in "Twice Upon a Time."
Trivia: This episode was originally titled "The Last Cyberman." The title was changed to something less spoilery after one of the guest stars forgot their copy of the script in a London cab. The script was swiftly returned, but the showrunners decided to change the title anyway out of caution.
The Pyramid at the End of the World - S10-E8
Trivia: UNIT, and its director Kate Lethbridge-Stewart, was originally going to appear in this episode, but actor scheduling conflicts prevented this - hence the Secretary-General of the UN and the three military officers.
Trivia: David Troughton, who plays Professor Hobbes, is the son of Second Doctor Patrick Troughton. He previously appeared in the classic series twice: alongside his father in "The War Games" as minor character Private Moor, and in the Third Doctor story "The Curse of Peladon" as King Peladon.
Trivia: Lynda Barron, the actress who plays shop assistant Val, previously appeared twice in the classic series: the singing narrator in "The Gunfighters", and Captain Wrack in "Enlightenment".
Trivia: The portrait of Queen Victoria visible in the soldiers' camp is not a portrait of the real Queen, but of her as portrayed by Pauline Collins in the Tenth Doctor episode "Tooth and Claw."
Trivia: The original plan for the episode was that the Doctor and Rose would both (in-universe, obviously) fake Scottish accents, and both drop them when things started getting interesting, leading to the locals realizing that they weren't who they claimed to be. The discovery that Billie Piper could not do a Scottish accent to save her life changed that quite quickly, although she did get to demonstrate her bad accent on-screen when Rose attempts to do one, and is swiftly told by an appalled-sounding Doctor to stop. As a final note, the Scottish accent that the Doctor puts on isn't actually David Tennant's real accent - it's a different Scottish accent.
Trivia: When Elton and Ursula come back after their "storming out" because Ursula forgot her phone, if you look closely, the headline on the newspaper Victor is reading says "Saxon leads in polls" - a sneaky reference to the villain of the next season, Harold Saxon... Better known as the Master.
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.