"Oh, say boss?"

[JohnM]

Why did the writers use this dialogue device so often? When Rochester phones Jack, they have a conversation, then Rochester says goodbye, but before hanging up says "oh, say boss?", and then they have a final exchange, ending in a gag and Rochester saying goodbye again, this time in his signature style.

The same device is occasionally used when another cast member phones, except they say "oh, say Jack?"

It's a curious thing. Is it to prepare the audience for a concluding gag, let them know it's coming? Like a a timing thing? Doing a small joke, then a medium joke, then saying good-bye--but WAIT--one last BIG joke.

[Mister Kitzel]

It must be a set up for a final joke just as you surmise. The writers may have even used the line as a device for themselves to know they had to end the bit with something better than the rest of the routine.

[marknyc]

This reminds me of another quirk that I always thought was interesting: sometimes Jack will say "what's that, Phil?" or "what's that, Mary?" but it doesn't seem to enhance the joke. In fact, it's usually a straight line that ends up repeated.

My theory is that it gave Jack's way of stalling while turning the pages of the script.

[Moose Hatrack]

In my listening I find that Jack asks, "What's that (Mary, Dennis, Phil)?..." when he senses that a straight line came in before the previous laugh subsided. By prompting the cast member to repeat the straight line, Jack ensures that the entire audience (home and studio) will hear it so the subsequent punch line will be more likely to succeed. When a punch line comes in too early sometimes Jack will come right out and say something like, "Wait until the laugh is over" or "Next time wait for the laugh". If the lost punch line was good enough you'll sometimes hear Jack throw a flag and do the whole joke over. That's that way I hear it anyway!