In the previous seasons, each episode showed a different scenario that deals with the social (and at times personal) implications of a "technological way of living". The use of technology was emphasized in each episode, introducing a big plot involvement of the "new media" such as YouTube, Facebook and Twitter, long before other shows embraced this media significantly in their stories (a show like "House Of Cards" comes to mind). This imaginative way of presenting contemporary and futuristic technology on screen, seems to drive the audience to watch and adore the show, even if for that reason alone.
However, I would like to suggest that the new "White Christmas" episode feels to be drifting from this theme ("technological way of living"). Aside from another episode which can be claimed about the same (S02 Ep01 "Be Right Back"), "White Christmas" focuses on more philosophical issues regarding mind-body problems, especially questions about the relations between thoughts and personality, rather than center the episode on the subjects they addressed before. Like many other Sci-Fi movies (this genre is always "on the verge" of leaping into philosophical questions), the technological presentation in this episode is mostly in the background, helping raising this kind of questions in a manner which is more clear and entertaining.
This observation is most obvious in the second story where Greta decides to literally detach her mind from her body, a thought experiment that is old as the practice in philosophy itself. More questions about the possibility, morality and purpose of why one would duplicate his mind into an electronic egg (what is this thing?) come to rise, rather than questions about how this kind of use of technology will function practically in society. There are a lot of elements in this scene showing the contradictions coming to thought about the possibility of this kind of split, and furthermore, if this kind of distinction between mind and body is even plausible. Nevertheless, I like how this scene shows how human suffering is not only imposed by social affairs and bodily urges such as sex, tiredness and hunger (she can't even feel those things), but even if you take all of this away, and just remain in a state of being in thought (we don’t know any other state), this alone can cause a great misery. I'm mentioning this of course, in regarding to the moment that Mathew chooses to drift the time in Greta's subjective sense of being. When Matthew pushes that button to advance in time for 6 month, you cannot but feel great empathy for the pain that Greta the electronic egg is going through. This scene reminded me the absurdity of the use of solitary confinement for prisoners, which implies that a prisoner prefers to be among rapist and killers rather than being in solitude with his own self and thoughts.
The first sub-story is less straightforward but can be similarly read. In this scene, Matthew is coaching Harry to hit on Jenifer at a party using a device, which allows Matthew to see, hear, and talk to Harry while he's making a move on her. At the beginning, we see how this kind of technology will come to use in practical terms, in a resemblance to the Google Glass we have today. But the cliché' twist in the end, that shows Jenifer as mentally ill, makes a turn as well in the way one should interpret this scene. Taking the plot to the route of insanity encourages the viewer to focus his attention to the comparison between the two characters, in how their thoughts come to mind, and the way they differ in that regard. How Matthew is more real than the voices in Jenifer's head? How can one distinguish a voice from a "genuine" thought? But these kinds of questions are mostly boring. For me, the comparison of the characters marks the fact that there isn’t a single voice in one's identity. The indecision of approaching to a woman in a party will sound about the same in Harry's head, even without Matthews's technological presence in his mind. This indecisiveness is always present in our everyday lives, expressed in a multiple voices arguing about different wants, in opposition to the notion of a single decisive intention which one can call "me."
To write shortly about the way identity comes to function in the third story, it can be seen how Joe constructs his child's gender and personality through imagination alone, only to discover to be wrong, and the child he was observing is not really his. Furthermore, in the end of the episode Joe confess his wrong doing of assaulting Beth's father, but like in Greta's case, the viewer realizes the whole confession was taking place only in Joe's mind. The following scene is suggesting that this kind of confession from a "cookie mind" copied from the original Joe is sufficient to convict him in court. So it seems that even the ending of this episode is mainly focused on the same mind-body problem as elaborated above.
I hope you enjoyed this kind of reading. I really think that in this "White Christmas" episode the Black Mirror creators maid a leap in asking more "deep" questions than they generally would. Whether or not it was successfully done is for debate. But I can surely say that for me, seeing this episode and reading it in that way was pretty enjoyable and entertaining.