The common criminal nick name of 'Five Fingers' is upgraded to 'Eighty-Eight Fingers' due to there being eighty-eight keys on a piano.
Because an anniversary song based on a variation of "Happy Birthday to You" would have raised copyright and royalty issues, the producers instead created an original anniversary song, which Barney and the police officers sing to the tune of "March of the Swiss Soldiers" from "William Tell" by Gioacchino Rossini. which is in the public domain.
The piano that Fred wants to buy for Wilma is a "Stoneway", a play on the name of the famous piano manufacturing company Steinway. In the German language the word for "stone" is "stein".
ABC originally broadcast this episode in black and white.
The short police officer talks like Jack Webb from the Dragnet radio play and then later on TV series.