When Lucy is trying to make it to the roof at the end of the movie the police officers go from having night sticks in their hands to having their hands facing palms out to stop the crowds.
(at around 1h 50 mins) As Jude is climbing the stairs toward the newsstand, he is wearing a gray boiler suit (coverall). When he pays for his paper and turns away, he is wearing a black jacket and black jeans.
During the school dance the one of the musicians switches from playing the keyboard to playing the drums in the same song.
When Max is playing golf on the roof the beer bottle used for as a tee disappears and reappears between shots.
While the characters are outside Mr. Kite's tent, the lighting and shadows keep changing from a mid-day light to a sunset-like light.
Military deaths are reported to family by two officers, one of which is a Chaplain. The personnel that tell Daniel's mother of his death are both Sergeants.
The armory which Max enters is actually located on 26th Street and Lexington Avenue in New York City. At the armory there is a gold "69" in the floor when you enter. It represents the Fighting 69th Regiment located in this armory. When Max enters the "69" is not visible.
In the "With a Little Help From My Friends" scene Jude is "handed" a joint, if you look closely his fingers are touching each other indicating they aren't holding anything. Yet a split second later he coughs out a puff of smoke. This is done because they were filming on Princeton University's campus and they weren't allowed to have actually drugs, so they mimed the joint instead. This is stated in the movie commentary. This was also done to keep the film from receiving an "R" rating.
The boy in the coffin during the "Let it Be" sequence is very clearly breathing.
When Lucy shoots the ball in the basketball scene of "It Won't Be Long", she ends up missing, but in the first shot of the ball hitting the rim, it clearly looks like it's going in.
The movie clearly takes place in November (hence Thanksgiving) in and around New York City and progresses from there, but snow is never seen. Also, it would be way too cold to be driving around with the top down in a convertible.
When Jojo is walking down the street after the businessmen "dance" his reflection is missing from the window behind him.
In the scene where the white women dance on top of the water and, subsequently, fall in, one of the platforms that a dancer (on the right side of the "v") is standing on is clearly visible, covered and uncovered by the waves.
A modern Merseyrail train can be seen crossing a bridge in the background of one of the Liverpool shots.
In the scenes taking place on the high school basketball court, there are floor markings for a three point arc. High schools did not adopt the three point shot until the 1980s.
Just prior to the song "Dear Prudence", Max is holding a box of "Cap'n Crunch" cereal with a modern design.
In the scene in New York's Port you can see a modern day ferry in the background.
As Jude exits the pub at the end of the film there's a (now commonly seen) security video camera pointed at the pub's entrance - something that wouldn't have existed in the era.
When Jo-Jo is playing guitar solo in "Come Together", it sounds like his Telecaster has a whammy bar, which it has not. He even mimes using it with his right hand. But with his left hand he doesn't even bend the strings.
While Max is fighting in Vietnam during "Helter Skelter" his M16 has a blank firing adapter installed on the end of the barrel, which allows the prop weapon to fire multiple rounds.
When Jude was in the first car of the subway during "Across the Universe", a crew can be seen in the window reflection on the right side of the screen.
The "Dayton" athletic field scene for "I Wanna Hold Your Hand" is filmed in Brooklyn's Red Hook section, in front of the former Port of New York Authority Grain Terminal. When the camera takes Prudence's point of view, the tops of lower Manhattan and Jersey City skyscrapers can be seen over the trees.
At the military funeral, the soldiers fold the flag wrong, as the stars should never face down. Soldiers would definitely know this.
During the "I Am The Walrus" scene, the man sings "coo coo cachoo" when the real lyrics to the original song was "goo goo gachoob".
After Jude gets off the boat and is speaking with his former girlfriend, her husband comes over and escorts her away. His wedding ring is on his right hand and not his left.
When Lucy quotes the opening lyrics to "I Am the Walrus", she says "I am me, as you are he, as you are me". The correct opening (as sung by Dr. Robert) is "I am HE, as you are he, as you are me".
When Jude and Max run into each other at Princeton and the books fly everywhere, they leave some papers on the ground.