This is the only episode in the series in which Martin (John Mahoney) was ever in Roz's (Peri Gilpin) apartment.
When Martin mentions wanting another dog, Frasier says 'Dad, I said you could have a goldfish!' Though no mention is ever made of Martin getting a fish, in "The Ann Who Came to Dinner" he mentions having an aquarium plugged into the same outlet as his TV, clock radio and a space heater.
The thick book propping up Frasier and Niles' engine in the auto classroom looks to be a McMaster-Carr catalog. McMaster-Carr is a private American supplier of hardware, tools and maintenance equipment.
The opera Frasier, Chelsea, Daphne and Niles are on their way to see is Richard Wagner's "Tristan und Isolde."
The scene title card, "Gentlemen, Meet Your Engines!" is a reference to the command given at the beginning of a professional automobile race: "Gentlemen, start your engines!"