That melody
It's a darned good thing Miss Froy is OK at the end, and can play the melody on the piano.
She hummed it so badly when conveying it to Redgrave's character, that it's quite different. She changes the rhythm, changes the tonality from minor into major (similar to the way it's changed for the ending credits), and is just generally out-of-tune.
He continues to hum it pretty much as she sang it, or even more degraded -- who knows how that would have changed the message?
Yes, I know it's the MacGuffin, and yes, I can suspend my disbelief and enjoy the film, and yes, I know many viewers would not have noticed, so no lectures, please -- it's just one of those things I can't help but hear.