The classroom set appears to be the exact same one used for "Welcome Back, Kotter."
This episode marks the last of the several "Fonzie-to-the-rescue's" in the series.
The title is based on the musical "Kiss Me, Kate". The original Broadway production of "Kiss Me Kate" opened at the New Century Theater on December 30, 1948, ran for 1077 performances and won the 1954 Tony Awards for the Best Musical, Book and Score.