Yes, in my humble opinion, the best, the ultimate "The West Wing" fan trivia question would be the following: There are 5 times during the series where, within the time frame of Bartlet's actual presidency, someone in close, personal conversation with him addresses him as "Jed", instead of the more formal and proper "Mr. President" or "Sir".

PLEASE NOTE: There are some rules/exceptions to this question. Obviously anyone who is related to Bartlet doesn't count, whether it's via blood or marriage (so for example when Doug Westin clearly calls him Jed, well that's the man's son-in-law, he's allowed, to, that's everyday stuff. The entire point of the question and what makes it interesting (I think) are the answers are what makes it so special of an act and almost unique, because it's so rarely done. And, on answer #3, yes Millicent the Surgeon General is Ellie's Godmother, I don't think it's unreasonable to not count that as an official relative, so that her moment would be a legit answer to the question.

It has to be an actual conversation that legitimately happened, so no, I do NOT count in the season 2 finale when Bartlet finds himself having a chat in his mind with a newly deceased Mrs. Landingham and she says "God Jed, then I don't even wanna know you" upon "exiting" the oval office.
You also might say, oh but wait, didn't Vice President John Hoynes refer to him as Jed once? Yes he did, but this was in a flashback scene to the night of the (1998, sort of technically) convention, Bartlet was asking him to be his running mate, so obviously their administration hadn't started yet, he was not yet actually the President.

And my final exclusion is from the season 5 finale "Memorial Day", Bartlet is running out onto the field at Camden Yards to throw the first pitch, and Leo shouts out "Jed!", but this was only to try and get his attention in a very loud and hectic moment, because what he had to tell him was so important. But they certainly weren't having a proper dialog with each other, Bartlet clearly never ever heard Leo say anything.

allllllllllright well I hope my little (?) list of disclaimers didn't just suck all the fun right out of this haha.. But I had gotten some initial feedback after uploading that the "rules" could've been made more clear. I hope all The West Wing fans enjoy this :)