Prior to the development of the measles vaccine in the 1960s, nearly twice as many children died from measles as from polio.
When Sister Monica Joan is in the barn and says 'Dost thou think because thou art a rat there shall be no more cakes and ale?' she is deliberately misquoting Sir Toby Belch in Shakespeare's 'Twelfth Night' ( replacing 'virtuous' with 'rat').
It is revealed in files that Sister Monica Joan was born Antonia Keville and became a Postulant in 1908. With the episode being set in 1960, and Sister Evangelina commenting that "she's nearly 90", it can be deduced that Sister Monica Joan became a postulant in her late 30s.
The scarf Sister Evangelina wears while searching for Sister Monica Joan is the same scarf that Jenny wore when leaving Nonnatus.