When Herman tells Lily he is being transferred to Buffalo, Lily says to Herman "Where they send you, I will go". This is an obvious nod to her role as Zepprah in Ten Commandments as she says exactly the same thing to Moses when he is told to go to Egypt by God.
Herman sings "Shuffle Off to Buffalo", a song introduced in the musical film 42nd Street (1933). The lyrics talk about going by railroad train "to Niag'ra in a sleeper" for a honeymoon. Niagara Falls, near Buffalo, NY, was long a popular honeymoon destination.