Marvel's gamble on the Russo brothers continues to pay off. Mainly known for cult TV comedies, they handle the massive budgets and expectations of superhero action films with aplomb. Much like Age of Ultron before it, Civil War needs to pack a lot in, and the hyperactive plotting of Arrested Development and Community turns out to be good training for making all the pieces fit together. An example: Spider-Man is introduced in something like five minutes. They also manage to craft the sequence where the Avengers finally start fighting each other into something genuinely engaging. It's of little surprise that they've been handed the keys to the Avengers films due for release in 2018-19.
Civil War only very loosely follows the framework set by Mark Millar's crossover, where superheros have to decide whether to register and become agents of the U.S. government. In the film, S.H.I.E.L.D. has been discredited, and the pressure comes from the United Nations, who wish to licence and legitimate Avengers interventions in sovereign countries (echoes of recent adventures in the Middle East and Africa are muted). Cap's reasons for resisting 'the Accords' is a bit woolly, and boils down to an intuition that he's more likely to call the shots right than the UN. Conveniently (given that it is his film) in the case of Bucky Barnes he is right.
The instrumental question about whether private citizens are better able to exercise their superpowers effectively than democratically-elected governments is a side-issue. More important is the debate about accountability. Superpowered interventions, even if they end up saving lives (or the world), nonetheless kill civilians. The villain in Civil War is after revenge for the death of his family by superhero activity in 'Zarkovia' in a prior film. It's a motive shared by the Black Panther in this film, and in the end the latter proves to be the true hero by letting go of the thirst to take an eye for an eye – something Tony Stark is unable to do. That said, Cap preference to be held accountable only by himself and his friends is troubling. A brave creative team would challenge it in future films.