In chase scene where they ride the bike down the steps is a reference to the "Odessa Steps" sequence of Battleship Potemkin where a baby carriage careens down the steps.
Judy imitates Humphrey Bogart, saying, "Of all the gin joints in all the towns in the world, he walks into mine. Play it, Sam," and then sings "As Time Goes By".
Madelin Kahn's opening cry of "Howard! Howard Bannister!" is a direct mimicry of the way Ruth Warrick says "Howard! Howard Graham!" at the start of this film.