The first time Jack appears in the hospital, the physician comes out of Joy's room and tells him Joy's left leg "snapped like a twig." It is her right leg which is shown collapsing and being treated throughout the film.
Jack and Joy actually spent their honeymoon in Greece, not that search for the "Golden Valley". Outside of his Army stint in WW1, Jack had never left England before and was unsure about traveling to Greece. He was afraid it wouldn't live up to what he had imagined. After reading Homer and Aristotle (in Greek) he had built up quite a mental image. The trip did not disappoint him.
Jack never learnt to drive, despite numerous attempts at learning.
Joy was treated for cancer at the Churchill Hospital in Oxford not in London as shown in the film.
Joy actually broke her leg at Jack's home, The Kilns.
Joy Gresham had two sons, David and Douglas, but only one son, Douglas is depicted in the film.
In one of the scenes in Magdalen College Chapel, a character is shown singing from a copy of the "New English Hymnal" which was not published until the 1980s. The descant to one of the hymns sung was also written later than the date at which the film is set.
As C.S. Lewis and Joy Gresham climb to the turret of the college in order to admire the Oxford skyline, a 1960s-style towerblock is briefly visible in the distance.
In one scene inside the college chapel, the choir are singing Sir David Willcocks's descant to Once In Royal David's City. That descant was first published in 1970, nearly 20 years after the film is set.
A member of the choir is seen using the New English Hymnal which was first published in 1986.
Both the picture of the Golden Valley hanging in Jack's study, and the actual vista Jack and Joy find on their honeymoon are in fact the view of the Wye Valley from Symonds Yat - as the woman in the hotel says, the Golden Valley is that of the River Dore.