The Semaphore Flags held by The Beatles on the poster (and album cover) don't spell HELP, but NUJV. This was done deliberately because the photographer of the cover, Robert Freeman, thought that it doesn't look good, therefore the flag postures were improvised, therefore it's not an actual error.
In the scene where Prof. Foot and Algerman are on the ski lift and try to kidnap Ringo off of the sled, the rest of the Beatles sled far away down the mountain while the ski lift is still going in the opposite direction. The rope breaks only after the lift turns around back down the hill, yet when Ringo stands up, The Beatles are just passing by.
When the attempts are being made on Ringo's life, he and John go to post a letter. There are people walking on the sidewalk in the background, and a time lapse has them jumping suddenly to another spot on the sidewalk.
When Prof Foot and Algernon kidnap Ringo in The Bahamas, they wrap him in a blanket before throwing him in the trunk of their car. A bit of the blanket gets caught when the lid closes, but when George jumps onto the trunk as car drives away, the bit of blanket is gone.
When the boys are out in the field protected by security, you can see through the whole first song, that Ringo does not have the ring on his finger, but during the next song before the ground explodes, he does have it on.
During the performance of "Help!" in the beginning of the movie, Ringo is wearing the sacrificial ring in the close-ups but not in the other shots. Also, in the close-ups, Ringo and his drums are on a much shorter riser than in the other shots.
When the boys are at the piano in the Alps at the end of the "Ticket to Ride" sequence, a hand appears on Ringo's right shoulder which obviously was a crew member giving the signal for the guys to leave. As the boys turn to leave and ride away, the hand is resting on the top corner of the piano.
Paul McCartney plays guitar left-handed (and has been known to play right-handed guitars upside down as he did with his Hofner bass) but the scene in the field where the Beatles are miming to their songs, Paul is holding his Hofner bass guitar as a right-handed guitar player would.
During the "Another Girl" sequence, when Paul is playing the bikini-clad girl beside him like a guitar, Paul suddenly looks embarrassed, and has a shocked smile on his face. If you look closely, he accidentally hits the left breast of the girl as he pretends to strum his girl guitar.
As mentioned in "Crazy Credits", during the opening credits each time a dart hits the projector screen a credit appears. The color of the credit matches the color of the dart, except for the "Produced by Walter Shenson" credit. (The dart is red but the credit is green.)
When Bhuta jumps out of the Good Year blimp to lay the plan to trap the Beatles, there is a wide shot of the stuntman playing Bhuta jumping out of the blimp. Watch the bottom of the screen, and you'll see the stuntman's head bounce back into the frame after landing on an obvious crash mat. So, the blimp wasn't as high in the sky as the filmmakers were trying to make it appear. Afterwards, there is a shot of a horribly fabricated dummy hanging where Bhuta is supposed to be hanging (too skinny, and the arms are too long).