It's about flights of fantasy. And the nightmare of reality. Terrorist bombings. And late night shopping. True Love. And creative plumbing.
Why it is hard sci-fi
Soft on the science, hard on the bureaucracy. Gilliam is rigorous about what a state run by paperwork actually looks like. Forms route everything. A typo causes an arrest. The technology is steam-punk pneumatic ducts and CRTs with magnifying lenses, all of which is stylistic, but the rules of the system are consistent throughout.
Science inside it
No real physics. The interesting model is information theory and queueing. Records reproduce. Errors propagate without correction. The film is a study of what happens when a society delegates judgment to a system that cannot revise itself.