As evidenced by Bart's chalkboard quote "If Villanova does not win we will lose everything" the day after the episode's airdate Villanova won their first men's basketball national championship in school history on a buzzer beater.
The title is a play on the film, 'The Birdcage,' in which Hank Azaria appeared using a voice very similar to the one he uses to play Julio.
When Jack says "of all the schools, in all the districts, I had to get transferred to this one" it is a parody of Casablanca's famous line "Of all the gin joints, in all the world, she had to walk into mine".
In the beginning of this episode, Bart writes "If Villanova does not win, we will lose everything". This could give insight into where Springfield is located. There have been many guess as to whether it refers to the city in Illinois, somewhere in Oregon, etc; however, if Villanova is mentioned, it would appear that The Simpson's Springfield could be located in Pennsylvania.