If you haven't seen it, the basic plot is: Arthur = spoiled millionaire child of a snobbish and distant father. Drunk most of the time, but you understand why when you see his family, and the woman he's expected to marry. She's the most wonderful Wrong Person Hero Is Engaged To I've ever seen. Unconditional love of the most stifling and horrifying order.
Her father abhors Arthur, but will force him to marry Susan, only to please his little girl. One of my favorite bits of dialogue in the movie is where Susan's father manfully says to Arthur: "When I was 11 years old, I killed a man." Terrified, Arthur replies understandingly: "Well, when you're 11 you probably don't even know there's a law against that."
Arthur will be cut off from all monies if he doesn't marry Susan, and having no useful skills he resigns himself; but then he meets Linda. He sees her shoplifting a tie, and when the guard follows her out of the store to arrest her, Arthur follows them out and saves her. Here's where I decided the movie was perfect, because in the five minute scene of him saving her with lies, and her going along with his lies, and then the first flirtation between Arthur and Linda, followed all the while by Arthur's butler, and then the first witticisms exchanged between Linda and the butler... you know that Arthur and Linda are meant to be together. [The scene isn't online, but here's a later scene from the movie.]
Sometimes you go an entire movie or novel not quite convinced that a couple is meant to be together. Once you're sold on this, you're sold for the rest of the movie (and the sequel) because you're rooting for them. They were so good together, they're one of the few movie couples you could imagine hanging a series on, like Nick and Nora Charles.
Billy Mernit, who writes about romantic comedy, agrees about the importance of being convinced over the rightness of a match:
"Romantic comedy writers all too often put way too much emphasis on figuring out ways to keep their leads apart. But conflicts and obstacles are actually the easy part of romantic comedy screenwriting. The harder task lies in creating what I call a chemical equation for your protagonists - presenting the clear, vivid and genuinely convincing evidence that because he's like this and she's like that, they absolutely, positively must end up a couple." (In his review of Just Go With It)
Georgette Heyer was aces at this too.