Actor Allusion: Paul's grandfather is frequently referred to as "clean" because the actor, Wilfrid Brambell, played a "dirty old man" in Steptoe And Son (which begat the American versionSanford and Son). These jokes would often go over American fans' heads, but British audiences would've gotten the references immediately.
And according to the extras on the DVD, Brambell was a meticulously clean and well dressed man in real life.
Steptoe And Son's Wilfred Brambell, who was reportedly included because the studio wasn't sure the Beatles could carry a film by themselves.
The television director is played by Victor Spinetti, who played the mad scientist Foot in Help!, and also appeared in the Beatles' Magical Mystery Tour.
The girl with Paul's Grandfather at the casino is Margaret Nolan, who was Bond's girl Dink at the beginning of Goldfinger (and appeared painted gold in the opening credits).
The Red Stapler: Demand for the Rickenbacker 360/12 12-string guitar skyrocketed after George Harrison used one throughout the movie.
Romance on the Set: George Harrison met his first wife, Pattie Boyd, while shooting this film. She played the blonde schoolgirl who says "Prisoners?" when Paul tries to flirt with her on the train.
Studio Hop: The film was originally a United Artists release, and was licensed from its original owner, American film producer Walter Shenson. After UA lost the rights in 1979, Shenson regained the rights to the film, and since then, three different Hollywood studios have released it: Universal Pictures in 1982, Miramax Films in 2000, and Janus Films in 2014.
In the very first shot of the movie, George accidentally tripped and fell, and Ringo accidentally fell on him. The falls and the Beatles' laughter about it lent the shot an increased sense of energy and motion, so that footage was left in.
John wasn't meant to be in the bathtub when George was teaching Shake how to shave, but when Lester found Lennon already there, they decided to work it in.
Director of Photography Gilbert Taylor said that the sped-up aerial shots in "Can't Buy Me Love" came about because the battery in his camera started to die, causing the footage to be "undercranked" and fast motion. When director Richard Lester saw the rushes of the footage, he immediately arranged for more sped-up aerial shots.