Much of the important dialogue is "throw-away" dialogue, in a sense. It's clear to the hearing, but lines are often spoken by the characters to themselves, for their own (and our) amusement, or delivered in very deftly choreographed "simultaneity," each speaker maintaining an independent point of view in rapid-fire repartee. Implications are understated. We are expected to expect the unexpected, to listen to every line.
The plot is composed like a piece of music. Each scene takes moment from the time-line established by the impending day and hour and minute at which a husband (Cary Grant) and wife (Irene Dunne) become legally divorced, and the movie ends at precisely the stroke of midnight which marks that moment. They clearly want each other back, but will they cleave together or cleave apart as the clock strikes midnight?
One extended "movement" of the movie lets Cary Grant charmingly undermine his wife's new relationship. In corresponding scenes later, Irene Dunne brilliantly plays a dumb floozie, pretending to be the husband's sister and demolishing in one evening his reputation and his prospects for marriage in respectable society. In these later scenes, in another of the movie's nice compositional touches, she does a reprise of a hoochie musical number performed earlier by a girlfriend of her husband's, and then falls into her husband's arms, apparently drunk. He gestures for her to look back and say goodnight to the horrified guests (and to us) as they do a wonderful little wobbly dance out the door, having burned their bridges behind them.
I found the opening few scenes of the movie unlikable, but with the entrance of Irene Dunne, the movie gets us on board. There's so much great understated visual and verbal double entendre (in the best sense) that I want to go back and see if there's more that I missed. In one scene, Cary Grant has brought to Irene Dunne's new fiancé the paperwork on a coal mine the divorcing couple still own. Interrupted by a visitor while advising the fiancé on where it would good to sink a shaft (har!), he explains that he and the fiancé (brilliantly played by Ralph Bellamy as a very successful bumpkin businessman) are transacting a business deal. The movie moves along briskly and doesn't play up the point, but we catch, for a fraction of a second, Irene Dunne squirming as she finds herself looking like the business transaction in question. The movie moves through moments like this quickly, with high respect for our intelligence and our capacity to get in on the joke.