When Jude is seen packing his stuff in his Liverpool bedroom just after finishing on the docks we can see a Liverpool FC poster on the wall mimicking the famous "This is Anfield" sign. The LFC crest design shown on that poster hadn't come into being in the 60's - in fact it's probably more at home in the late 80's.
In the scene where Sadie is in the dressing room, she takes a drink from a bottle of Jack Daniels. The neck of the bottle has black plastic on it. In the late 60's, Jack Daniels was sealed with paper tape across the top of the bottle.
When the two girls are riding bicycles toward the home where they see their mother get bad news, there are modern fiber optic TV cables on the poles around the street. The strain relief loop is highly visible.
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.
(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.
Dr. Robert's bus, when it's rolling into town and when it's on its way to Dr. Geary's place, has two separate cloth chairs on the back of it, but when it pulls away from there without Jude, Lucy, etc., it has a love-seat.
During the "Strawberry Fields Forever" sequence a shot shows Jude's foot splattered with bright red paint. Once the shot cuts away and back, the paint disappears. When the shot then cuts away and back a second time the splattered paint is on his foot again.
During the "It Won't Be Long" sequence in Lucy's bedroom with her sister and her sister's friend, the young girls are laying on the bed holding a bowl of popcorn and singing backup to Lucy, in the next shot, when Lucy joins them on the bed, the popcorn has dissolved into thin air.
During the "Strawberry Fields Forever" sequence, when Jude first starts to paint the big strawberry, his right arm is behind his head before he starts to paint. His arm crosses his body to the left and when the camera shot is zoomed out, his right arm is behind his head again.
When Lucy and Max sit by the water at the start of the "Blackbird" sequence, she sees a charred piece of wood floating in the water, presumably the one that Jude used to draw her portrait on the side of the building. From behind, we see her reach down to pick it up, but from the degree that she bends over, she reaches somewhere just below her knees. Subsequently, we see from the front that she is sitting 4-5 feet above the water and could not have retrieved anything from the water with the shown action.
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.
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.
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.
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.
The accordion player in Mr. Kite's band is obviously not playing any of the left-hand bass buttons. Instead, his thumb is on the bellows release button which allows him to open and close the bellows without actually playing any notes on the instrument.