HILDY: A big fat lummox like you hiring an airplane to write: "Hildy, don't be hasty. Remember my dimple. Walter." Delayed our divorce twenty minutes while the judge went out and watched it.
Walter very rarely says how he feels directly. He's willing to spell it out in skywriting, though. You could see his action throughout the film as similar indirection; he's always telling Hildy he loves her by sending Bruce to prison, or by insisting she come back to work for him. Like the skywriting, it's cute… and also annoying.
HILDY: Do you know what it is? It's an engagement ring.
WALTER: Engagement ring?
HILDY: I tried to tell you right away, but you would start reminiscing.
Hildy has to show Walter the ring to get him to realize she's getting married. He talks so much he makes communication difficult—especially when you're trying to tell him something he doesn't want to hear.
EVANGELINE: What does he look like?
WALTER: That guy in the movies, Ralph Bellamy.
Walter is pointing out that Bruce looks like Ralph Bellamy—the actor who actually plays Bruce. This is a joke directed at the audience; Walter is really speaking to you, watching, not to Evangeline. There are a number of jokes like this in the film. They're a reminder that all the quick conversation and joking here is not necessarily meant to communicate from character to characters—it's meant to entertain you, the audience. And that, in turn, points out that a lot of Walter's talk (and Hildy's) is meant to entertain each other. They're flirting, and trying to impress one another. The talk is like spreading peacock feathers—what it communicates isn't anything so much as, "I am pretty and appealing, aren't I?"
WALTER: Wait a minute, wait a minute, aren't you going to mention the Post? Doesn't the paper get any credit?
HILDY: I did that. Right there in the second paragraph.
WALTER: Who's gonna read the second paragraph? Listen honey, for ten years, I've been telling ya how to write a newspaper story and that's all I get?
Walter is claiming that he taught Hildy how to use words. He's her mentor, he says. In a film in which words are so important, that tells you who Hildy's going to end up with.
WALTER: Don't worry about the story. Hildy will write it. She never intended to quit. We're getting married.
Walter here announces his marriage to Hildy—not to Hildy herself, but over the phone to Duffy! This shows just how much Hildy has given herself up to Walter—she agrees to marry him again without him asking directly. But it also shows again Walter's odd reticence. He's more comfortable speaking next to someone than he is speaking to them. Maybe he's not quite as secure as he appears. He may have been afraid, even at this point, that Hildy would say no.