I haven't answered the door in just a diaper, but I've had a couple of emergency middle-of-the-night frantic searches for pants when the dog starts throwing up or the smoke alarms go off, or a thunderstorm starts up, and I'm worried one of the kids is going to burst into the room. This is less of an issue now that they're a bit older.
I also go trapped in the living room of my old house a couple of times when someone came to the door, and I was down there, in just a diaper, because the staircase going up to where my pants were, was in view of the front door. It wouldn't have mattered if it was the Publisher's Clearinghouse with a $1 million prize, I was not going to answer the door in a big pink diaper. In this house, we have a second, back staircase, so now I have an escape route if I'm chilling on the main floor in baby clothes and someone rings the bell that I can't ignore.
I also got called down from my office to the kitchen to "look at something" by my wife... I was wearing just a t-shirt and a diaper, but I had light pajama pants with me and, thank God, I decided to pull them on, because she hadn't mentioned that what she wanted me to look at was samples that a window covering rep was showing her of various blind designs and materials. So, I showed up in the kitchen in pajama pants over a big plastic diaper... and there's this well-dressed lady from the blinds company waiting for me. I positioned myself across the island from her, so that my lower half was obscured, but man, I was never more self-conscious about the crinkling, which sounded like it echoed to me, although I know that most people don't hear it. I nodded politely for a couple of minutes, then said that whatever my wife wanted was probably fine with me, and then I turned tail and slunk out of there under the withering glare of my spouse. I maintain that that situation was her fault - a little warning would have been nice, she knows I usually work in just a diaper if we're not expecting anyone.