Continuity mistake: There is a scene in the movie where the Beatles enter a limousine, I believe at the beginning of the movie. In this particular scene the Beatles are all dressed in suits and ties, but when the Beatles are filmed in the limo, John Lennon is wearing a turtle neck sweater beneath a blazer.
Continuity mistake: While looking for the canteen, George inadvertently wanders into a production office. The receptionist takes George in to see Simon, who believes George is there to audition for a testimonial for those "dead grotty" shirts. While the receptionist is sitting on Simon's desk, her legs are straight. After Simon says, "Because he isn't wearing one of these nasty things", her legs are instantly crossed.
Continuity mistake: When Paul's grandfather goes to the queue of girl's waiting to see the Beatles, he offers free autographed pictures. As he is mobbed he yells "Oh me bum....me hat.". We see his hat has been taken/knocked off as some bobbies come to break it up. A quick cut to a different angle and grandpa's hat is back on his head.
Other mistake: When the Beatles are playing cards and singing "I Should Have Known Better," Paul (who shouldn't really be singing anyway) flubs the first line of the last verse. He sings "I sh... [laughs] never realized..." John does almost the exact same thing when they sing "I Should Have Known Better" in the concert scene.
Continuity mistake: As The Beatles leave the train Paul goes through the first limo and we can see the second limo he's running to with a bunch of photographers standing at the side of it taking pictures. In the next shot the photographers are standing in front of the car and not taking any pictures.