Continuity mistake: Toward the end where the guitarist comes to talk to the kid at his house. He turns the chair around to sit in it backwards, but throws the shirt down onto the ground. When he sits down the shirt is back on the chair.
Factual error: The airplane that Penny Lane is on has small vertical stabilizers on the wingtips, which were not designed into commercial jets until the early 90's.
Factual error: This is a wardrobe error... in the next morning scene after William has been deflowered, he is still in his Fruit of the Looms, which have the name printed on the elastic waistband. Fruit of the Loom did not print their name on waistbands like this until the 90s, in the 70s they just had single blue and yellow stripes.
Continuity mistake: When Russell and William are walking together to "find something real" the VW bus containing the "real Topeka people" drives by behind them 2 times over their left shoulder before pulling up to them a third time on the right side.
Factual error: It's 1969 at the very start of the movie, and William Miller is looking through a bunch of awesome vinyl records that his sister has given him, including stuff from Cream, Jimi Hendrix, and Bob Dylan. In the stash is Joni Mitchell's Blue. Blue did not come out until 1971.
Continuity mistake: In the scene where William is sitting in the tub working on his notes, after Penny comes in and sits on the toilet, he scrambles out of the tub and most of the notes which were on the side of the tub fall on the floor. In the next cut when the camera is positioned near the bathroom door, looking in, all of the notes are back on the side of the tub and none are on the floor.
Continuity mistake: In the scene where William first meets the Bandaids, Black Sabbath comes around in a limo and a couple of the Bandaids touch the windows while they drive around to go down the ramp. Then another shot shows the Bandaids look at the car go around them again.
Factual error: In the radio station scene, the closeup of the turntable tonearm shows a P mount head-shell and Stanton 500 cartridge. Neither was available until the mid 1980s.
Other mistake: When Russell Hammond goes to William's house he spots a professional photo of William and his sister Anita. The photo shows William as a 15 year old with his sister. But Anita has been away working as a stewardess, and has not seen William since he was 11 - who was played by a younger and different actor in those scenes.
Continuity mistake: Right after the scene in which the band has a fight over the T shirts, which Dick says is the band's first T shirt, you see Russell and William go to a house party in Topeka. One of the attendants of the party has a Stillwater shirt that is of a different design than the shirt first revealed at the show only minutes prior, which again was supposedly their first shirt. The shirt seen on the partygoer can also be seen later in the movie.
Audio problem: When the band is in the limo coming into NYC, Jimmy Fallon gives the band a quick pep talk (e.g., "all you can do is be yourself and leave a pint of blood on the stage"). When the shot changes from inside the limo to outside the limo, the audio does not match the movements of Jimmy Fallon's mouth.
Continuity mistake: In the scene where Russell jumps off the roof into the pool, you can see that two people from the top left corner jump into the water to save him; then in the next shot you can see that no one has jumped in because the surface of the water is undisturbed and then the same people jump in again.
Continuity mistake: While the band are talking about what William wrote about them in Rolling Stone and Russell is lying on the bench, the bag on his head has a white label which appears and disappears between shots.
Factual error: In the Cleveland scene when the band is playing you can see the drummer is using a quad beater (the thing that strikes the bass drum) on his drum pedal. These were not available until the 1980s. Similarly the rest of the cymbal stands and hardware is far too modern.
Continuity mistake: In the radio station scene, when Lester Bangs is pulling albums from the shelves and tossing them on the floor, he pulls Yes' Fragile and tosses it. In the very next shot, it's back on the shelf. Two shots later, it's back on the floor - or some other time-warped dimension, but not on the shelf.
Factual error: When William runs into the street to look for Penny Lane, he runs between a row of taxi cabs. Across the street is a blue mid 90's model GMC Suburban. Since the scene takes place in 1973, this is obviously a mistake. It may be necessary to use zoom, depending on the size of your screen.
Continuity mistake: Backstage at the first concert, William is sitting alone writing when Penny comes to talk to him. She has her glasses in her hand as she frames his face to guess his age. As the scene is shown from different angles, she is shown both with the glasses in her hand and without them in her hand depending on the shot.
Continuity mistake: After Russell gets William into his first concert, his rectangular backstage pass is pasted to his left shoulder. Penny Lane shows up with a round backstage pass, and by the time the camera's back on William, the shoulder pass has disappeared.