Like any great work of fiction, cinematic or print, "A Christmas Carol" begins with all the elements that will be used throughout the rest of the story. Moffat sets up three concepts around which the rest of the episode will be structured: intertextuality, self-reflexivity, and whimsy, all in service to the hopeful message that Christmas is a symbol for being "halfway out of the dark."
Intertextuality, a term coined by literary theorist Julia Kristeva is "The need for one text to be read in the light of its allusions to and differences from the content or structure of other texts; the (allusive) relationship between esp. literary texts" (OED). I take umbrage with the Oxford English Dictionary's contention that this allusive referentiality is somehow more the purview of literary texts. I'd argue that Science Fiction trumps many literary works for being intertextual. Doctor Who is often intertextual, but "A Christmas Carol" is a mix of both the obvious intertext--we are fully aware from the title credits onward that the episode will be a riff on Dickens's Christmas classic--and the less overt intertext in the face spiders, which sound suspiciously like the face huggers from the Alien franchise. And then there are the countless intertexts of how time travel can affect the past in an immediate way in the fictional present, from James Blaylock's "Lord Kelvin's Machine," (which would prove a very prolific intertext with this episode, since it concerns changing the past to change the villain's disposition), J.M. Frey's Triptych, to movies like Back to the Future and Looper. Dressing Dickens's A Christmas Carol in Whovian garb reminds us that it is a pre-SF tale of time travel. Scrooge is given visions - he does not actually travel through time, but then again, neither does Michael Gambon as Kazran Sardik, this episodes' science fiction Scrooge (whose father, also played by Gambon, looks very much like Charles Dickens). Sardik too, only receives visions and new memories - and it is in the reception of those visions that the program engages in numerous self-reflexive moves.
Self-reflexivity in literature is the idea that the text is aware it is a text. In cinema or television, it conveys a sense of the film or show being aware of what it is. This is sometimes overt, as in the breaking of the fourth wall in a program like Boston Legal, when characters spoke of the addition of "new characters" at certain points in "the season." At other times, it is subtle, like the many inside jokes Matt Smith and his companions make, winking at the camera without actually winking, as in the brief moment we see the young Kazran wearing a Tom-Baker-era scarf. But less often, it is even more subtle, as when "A Christmas Carol" uses Michael Gambon's gaze as the eyes of the audience, watching his past as projected image. This is an echo of Amy Pond speaking the words we are all thinking in the opening: "He'll come. He always comes." But Kazran becomes our mirror for laughter and tears: we know when it is time to cry, for Gambon's teary gaze tells us it is so. When his childhood self and the Doctor are threatened by a flying shark, he yells what we want to yell: "Run!" It's a lovely moment, reminiscent of Don Quixote standing in a bookshop holding a copy of Don Quixote. We are watching a character on an episode of Doctor Who watching an episode of Doctor Who.