"Lorelei the First", Richard's mom and Rory's great grandmother, is mentioned in this episode in past tense. However, she shows up in later episodes alive and well.
In the scene where Lorelai is guiding the twin brides and their mother on a tour of the Inn's grounds before the wedding, one of the ladies loses a shoe on the wooden bridge and it can be seen in the background as the mother is telling the twins that if they want pink and blue flowers, they can pay for them on their own.
The doors to the locker room at Richard's country club , which he and Rory enter after golfing, are actually the doors to the old pool room at the Graystone Mansion where the Chilton high school exteriors were shot.
Emily's feigned enthusiasm to join Rory and Richard to look at the "Mencken book" is an obvious ploy to leave Lorelai alone in the drawing room. Mencken was a vicious social critic, of whom people like Emily were a favorite target.