The episode title and plot is a reference to the film My Dinner with Andre (1981), which consists almost entirely of two men conversing in a restaurant.
This episode is a perfect example of how each story of the series evolves like a short stage play: all the action takes place on one set, there's an overarching theme that runs through the whole story, ensemble characters come and go establishing mini-plots and side conflicts, and an ultimate resolution of everything in the end, finishing with a fade-out. Another subtle homage to live theater in this episode is that it's broken into three acts, with a short fade-out between them.
Frasier (Kelsey Grammer) and Niles joke about Niles potentially being a closeted gay man. In real life David Hyde Pierce is openly gay. After Frasier jokes about who's going to tell their father, Pierce breaks the fourth wall and quickly looks directly at the camera as he sips his coffee.
This is the only episode of the entire series in which Niles' name appears in the title.
Martin (John Mahoney) mentions that "last Sunday was my birthday." Based on information in season five's The Gift Horse (1997), this means Martin turned 61 the previous Sunday.