A Hard Day's Night/WMG

A Hard Day's Night is a Documentary about The Beatles.
And everything in the film really happened.

Yes, there does appear to be counter-evidence, but this theory was once popular among a certain class of film reviewer.

Norm mistakenly thought John's Aunt Mimi was John's mother.
This explains why he says "John, put those girls down or I'll tell your mother on you."

It's an understandable mistake. For most of John's childhood, Mimi acted more like his mother than John's real mother did.

Paul McCartney is on a Mission from God.
He said that his mother asked him to look after his grandfather. His mother had, in Real Life, been dead for eight years when this film was released. Clearly, there was some higher purpose... Though we never do find out what it is.

Paul's Grandfather broke up the band
We see in the film that he made Norm and Shake have the first fight in their entire friendship. He probably made a similar remark to John or Paul somewhere down the line and ended up making them grow tension and eventually split.

John's line about visiting Harrod's is connected to his mother.
"I say, did you go to Harrods? I was there in '58, you know." John's mother died in 1958 -- the "'58" John mentioned.