There are dozens and dozens of references to Mary Poppins. Here are the main ones: Obviously, the nanny Shary Bobbins.
The episode title is a pun on the song, ''Supercalifragilisticexpealidocious''.
Request for a nanny through song.
Shary Bobbins' entrance, flying with an umbrella.
The walk in the park, meeting a one-man band, and flying kites.
A tea party on the ceiling is mentioned.
The songs, ''Cut Every Corner'' and ''A Boozehound Named Barney'' parody ''Spoonful of Sugar'' and ''Feed the Birds'' respectively.