When they were standing over the judge to be divorced, Walter hired a skywriter to write in the clouds,

Hildy. Don't be hasty. Remember my dimple. Walter.

The judge delayed the divorce twenty minutes to go out and read it.

First of all: what a terrible judge. Can't the judge stay on task? Can't the just read an eight-word message in less than twenty minutes? Someone should fire this moron.

Second of all: that big, flamboyant, self-aggrandizing message is a good summary of how Walter interacts with Hildy throughout the film.

He uses language not so much to communicate with her as to delay her. And he loves using technology to misdirect, and to say things he can't get away with otherwise. For instance, Walter yells at reporter Butch's fiancée for keeping him away from the paper:

WALTER: Now listen, you ten-cent glamour girl. You can't keep Butch away from his duty!... What's that?... You say that again, I'll come over there and kick you in the teeth!

(Which, to be fair, is something he probably wishes he could say to Bruce for taking away Hildy.)

Walter even tells Hildy they're getting remarried on the phone —and not even on a phone call to Hildy herself. He's talking to Duffy, the copy editor, and casually mentions the upcoming nuptials:

WALTER: She never intended to quit. We're getting married!

To which Hildy responds, 

HILDY: Can we go on a honeymoon this time?

(This relationship dynamic is weird.)

As adorably antique as it seems now, telephones in 1940 were examples of up-to-date technology; they were modern, forward-looking, and exciting. They fit right in with Walter's rapid-fire, hip dialogue, and suggest a futuristic world in which everything is sleek and speedy.

And Walter's mastery of that world is demonstrated when he uses it to slow the equally fast-talking Hildy down—his technology beats her train to Albany.