Hey, It's That Place!: The block of flats where Clara's family are having Christmas dinner is the same one used in some shots of the Powell Estate in "Rose" (in particular, the long walking sequence leading up to the "turn of the Earth" speech).
History Repeats: Matt was recovering from a nasty leg injury while filming the final episode of his tenure. David Tennant also filmed his final episode while recovering from an injury, his being an ailing back that he'd recently had worked on with surgery.
Milestone Celebration: Though the episode is primarily a Christmas special, it also happens to be the 800th episode of Doctor Who, and a big one at that — the Eleventh Doctor regenerates and the Twelfth Doctor takes over from here as the first of a new regenerative cycle. On top of all that, it also closed the franchise's 50th anniversary year.
The Other Darrin: Clara's father is played by James Buller in this episode, while previously in "The Rings of Akhaten" he was played by Michael Dixon. Of course, it works here because Clara's dad is 8 years older.
Real Life Writes the Plot: Matt Smith shaved his head for his role in the film How to Catch a Monster over the preceding summer and his hair hadn't grown back enough to replicate the Doctor's coif, forcing the actor to wear a wig. Steven Moffat incorporated this into the story, not only providing the episode with a number of gags, but also the fact the Doctor is wearing a wig allows for the direct resolution of a major dilemma faced by the characters (how the Doctor was able to recall the TARDIS without a key on his person).
Throw It In!: Matt Smith shaved his head for a role in the film Lost River, and it did not grow back in time to reform his Doctor's signature coif for his final episode. He shaved his head again for a bald cap and donned a wig. A script re-write incorporated the wig into the story, leading to several of the episode's funniest moments.
Written-In Infirmity: The Doctor start walking with a cane and a limp midway through the episode; in real life, this is due to an injury Matt Smith suffered. As SF Debris joked, Moffat was lucky Smith hadn't lost a limb or two by this point. Ironically, the reason the Doctor walks with a cane is because he actually does lose a leg during his time on Trenzalore, but references to this were cut from the final script (though maintained in the spin-off short story collection, Tales of Trenzalore.)
Dan Starkey (Strax) as a pair of different Sontarans. Although Starkey has been playing different Sontarans on screen dating back to 2008, this is the first episode since the introduction of Strax in which he has appeared as different Sontarans.
What Could Have Been: Steven Moffat originally had plans for an entire Series 8 with the Eleventh Doctor set on Trenzalore, but Matt Smith's decision to step back after the end of Series 7 threw a kink in that plan. Time is essentially most of Moffat's ideas for that Series 8 condensed into an hour long episode.