There are many themes that the film explores that are classic expressions of the Jupiter-Uranus archetype: sudden rapid success and expansion (the "Striking It Rich" archetype), celebration of technology, success with technology, the celebrated genius, successful rebellion/revolution, the quantum leap to overwhelming success, the successful birth, the arrogant rebel, etc.
Also, the whole energy of the film has this quality of manic electricity which can be a form of the archetype. I've heard Rick Tarnas use the word syncopation to describe the editing style used by Oliver Stone, and he connected this to Stone's Sun-Uranus square aspect. Similarly, I think David Fincher, who also has Sun-Uranus (a conjunction), achieves an electric syncopation vibe in this film. Syncopation is achieved when the musical note (or film image) that is expected is replaced with an unexpected surprising note (or image). The effect is one of unexpected movement and excitement that keeps you on the edge of your seat delighting in the next quick-cut surprise. The movie just carries the viewer along with its energetic backbeat pulse, and it has a classic Uranian "wow" energy.
What is somewhat puzzling to me is that Mark Zuckerberg has an unaspected Uranus. We don't have a birth time for him, and so it is possible that he has Uranus rising, or Uranus at the Midheaven, but without the time we can't know. There are a number of aspects in his chart that fit qualities that the film conveys. His Mercury-Pluto aspect really fits his powerful intellect, as well as the power dynamics he gets into with his mind and self-destructive communication style (his sarcasm) and his being a part of a mass scale (Pluto) communication tool (Mercury). The Mercury-Pluto alignment also fits his controversial (and secretive) impulse towards control of Facebook members private information. The strong Saturn alignments (conjunction to Moon and Mars, opposition to Venus) potentially fit his being known for having controlled/armored personality (as well as his groundedness and serious work ethic). But that Uranus is a bit of a mystery to me. It is tight on the Jupiter-Saturn midpoint, but I expected it to be more strongly aspected. Hopefully we will get his birth time at some point, and more will be revealed.
All charts are cast for noon (no birth time) and are based on birth data from Wikipedia.