The opening guitar riff at the start of the movie, with the boys getting chased by fans in a pure expression of what Beatlemania was really like. Rock'n'roll movies were never the same after that.
In fact, at least one historian called that riff "a starting gun for a new era of rock'n'roll."
And nobody can agree on exactly what chord it is. Entire armies of guitarists keep trying to repeat it.note It's basically a G9 with an F in the root position, played on a 12-string electric, but that's not quite it, because it's two guitars at the same time, and they aren't both playing the same voicing. Try playing (from the bottom string up) FCFACG and you're getting there.
The video performance of "Can't Buy Me Love." Just the lads goofing off on a field. A thousand music videos can trace their origins back to this.
The Oxford English Dictionary's entry on the word "grotty" cites John Burke's novelization of this movie as the earliest example of the word in print. Since Burke's novelization was based on Alun Owen's script, which in turn was largely based on the Beatles' own conversations, this means that the band officially added a word to the English language with this movie.