At least one color TV at the appliance store, seen showing a Cap'n Crunch commercial, was not made until the late 1960s. Some of the TV sets and appliances are much older than 1964, but appliance stores often sold trade-ins in that era.
When the bass player visits Disneyland he rides in a Matterhorn car. The Matterhorn cars in the 1960s were single bobsleds, not two tandem bobsleds as shown in the film. They didn't run tandem until the ride was updated in 1978. The ones shown in the film are the current tandem bobsleds painted in the 1960s scheme. Also, when he poses for a photograph with Mickey Mouse, Mickey is wearing a 1960s costume with a 1990s head. Mickey's hairline in the '60s came down to a point between his two eyes with much fuzzier hair. In the '90s, Mickey's hairline came to a point much higher on his forehead.
When The Wonders perform on a circular stage mocked up to look like the record of That Thing You Do, the "label" on the record has a copyright notice at the bottom. This notice has the C in a circle followed by the year and Playtone Records. The problems with this are (1) recordings could not be copyrighted in the U.S. until 1972, and (2) after they were made copyrightable, the correct mark for a "phonograph recording" copyright was a P (or more correctly, a record should bear both a P and a C). Prior to 1972, the label art was the only copyrightable portion of a record so the records (or to be more specific... the 45rpm singles) bore either no notice at all or a notice bearing the words "All Rights Reserved." The same label is on the record held up by The Wonders in the photo shoot at Playtone Records.
(At 1:30:00, Director's cut) While the Wonders are in the booth for the early morning "interview" show in L.A., as the camera pans around the DJ, the back of the Canadian pop LP Fields of Fire, released in 1988 by Corey Hart, is visible at the back of the stack of LPs.
When the photographer at Playtone says to Sol Syler "Saw you at Chasen's with Suzanne Pleshette," he raises the camera and takes a shot with it. His eye is nowhere near the viewfinder of the camera - it's behind the flashgun.
After reading a Telemart ad, Guy's father says that he's not sure he wants to live in a country where you have to do business on Sunday. Pennsylvania "blue laws" in effect during the 1960s would have made it impossible for him or Telemart to do business on Sunday.
In the recording studio, after Guy plays his solo "I am Spartacus", Del comes in. He says, "Let's play that Spartacus number again". Guy goes on to play something that bears no musical resemblance to the solo.
At the Mercyhurst College Talent Show, right after the song when the emcee is saying "Oh, my goodness!", in the back you can see Skitch Patterson has stood up, but half a second later, you see him sitting when Jimmy tells him, "That was way too fast, man."
At the talent show, the girl who sells tickets (wearing a blue dress) can be seen dancing in front of Jimmy near the stage, but at the same time we can see her selling tickets near the entrance watching the band (with Chad) wearing a different dress. (Technically, she must be playing two different people.)
When Guy is playing his drum solo, "Spartacus" at the recording studio, when he is finished playing he holds the cymbals so as to quiet them and then he lets go of them. When the recording master asks Guy what he calls his solo, and the camera pans back to Guy, he is once again holding the cymbals.
When the bass player visits Disneyland he rides in a Matterhorn car. In the beginning of the scene, he is in the rear of the front tandem bobsled, followed by Mickey, two marines, and Goofy in the rear tandem bobsled. At the end of the scene, he is in the front of the front tandem bobsled, Mickey and a marine are in the rear of the front tandem bobsled, and two marines and Goofy are in the rear tandem bobsled.
The ending lyrics of the song are sung differently when they record the song in the church and when they first hear it played on the radio. (it's the word "thing" in the next to last line of the song).
When leaving the Wisconsin State Fair and learning that their record has hit #7 on the charts, Lenny asks if they get a gold record. Guy tells him they need to sell 500,000 copies. In 1964, 500,000 copies was the sales plateau for an LP to go Gold, but the sales plateau for singles was 1,000,000 copies. It was not until 1989 that the sales plateau for singles was lowered to 500,000 copies.
During the montage of scenes from the state fair tour, we see an audience shot of the audience giving the Wonders a standing ovation. The lead singer for the Chantrellines is clearly visible in the middle of the shot. (The other acts would never be in the audience).
Lenny does not miss his cue at Villipiano's on "All My Dreams", he is making reference to the loud airplane flying over "the spaghetti place out by the airport" that they have gotten their first gig at.
The goof item below may give away important plot points.
When Faye is cutting Jimmy out of the Polaroid photo from her make-up case, you can see the back side of the photo is gray. Black and white Polaroid photos had white backs until the 1980s, when Polaroid introduced a new B/W style film that had gray back.