Some shots of the bus driving along country lanes were obviously shot at a later date, when the bus was empty. In The Beatles "Anthology" book, Neil Aspinall describes taking the bus back out on the road after filming had finished, to shoot some external links which had been forgotten.
Throughout the bus tour, George Harrison wears a fedora-type hat with a wide band. When the passengers file into the cabaret and take their seats, he wears a wool/tweed driving cap.
When Jimmy addresses the bus from the front, the next shot has him in his seat behind the driver.
Due to the semi-improvisational nature of the film, there are a lot of deliberate mistakes in continuity and plot.
Halfway through the staircase scene at the beginning of "Your Mother Should Know," John loses his balance and nearly falls off the step. He recovers, however, and the shot continues.
Paul loses his timing towards the end of "Your Mother Should Know"
John Lennon jumps up from his piano at inappropriate times during "I Am The Walrus"
During the title sequence, a camera is reflected in window during a shot of a seaside town.