Rory speaks of Luke and says to Lorelai "You called him Duke for two years just to make him mad." Originally, the diner owner was supposed to be a woman named Daisy, but was then changed to a male character. According to Amy Sherman-Palladino, she just changed the name and didn't make any changes to the dialogues. In another interview, Scott Patterson said that the second dialogue he got for the audition had his character misspelled as Duke (instead of Luke). Rory's line seems to be an inside joke about that.
After being located just beyond the kitchen area for the first season on, the bathroom in Luke's place has moved to the other side of the apartment near the bedroom area. It remains there for the remainder of the series.