When two of the Temptations are discussing their success, we are shown a date of 1964, but the car parked directly behind them on the curb is a 1966 Ford. Unlike today, in 1964, all new car models were still very closely guarded secrets and prototype models were kept draped at the factory until the release date, usually September or October previous to the model year.
In a scene that's labeled "New Years 1964" the guitarist in the backing band appears to be playing a Gibson Les Paul Custom as evidenced by the block fretboard inlays. The guitar appears to be red or sunburst; both finishes that were unavailable on the Les Paul Custom until after the Les Paul had resumed production in 1968. Prior to 1968, the Les Paul Custom was only available in black. It is feasible that the guitarist in the backing band, may have refinished a black Les Paul Custom in red or sunburst but it is highly dubious.
In the opening concert scene, the bass player is seen playing a Fender Jazz bass. The year is given as 1958, however the Jazz bass wasn't introduced by Fender until 1960 as the deluxe model, and it wasn't available in champagne pink until the mid 60's.
During the scene when the Temptations were recording "Papa Was a Rolling Stone" - the actor playing Dennis Edwards is shown singing parts of the song that were actually sung by Richard Street. In the actual song, Richard Street sings the part toward the end of the 2nd verse, "Heard some talk about Papa doing some store front preaching / Talkin' about saving souls and all the time leeching / Dealing in debt and stealing in the name of the Lord." Richard also sings lead during the 2nd chorus - and sings these lines during the 3rd verse, "Hey Mama, folk say that Papa was never much on thinking / Spent most of his time chasing women and drinking." Yet, in the movie, the actor playing Dennis Edwards is shown singing all of these parts.
When the Temptations are touring and performing at schools, many members of the audience are just shuffled between the first trip and the second trip a couple of years later and they are wearing the exact same clothes.
When Otis gets off the bus and "Ooh, Baby, Baby", is playing, he eagerly gets out to find his wife, Josephine. His hair is permed, which had been discussed in an earlier scene at the beginning of the movie. But the next shot when he does find his wife, his hair is not permed.
In the movie, Otis Williams is portrayed as more devoted to the mother of his children (Josephine) than is factually accurate. Otis Williams himself admits in his autobiography that he had romances with several women during and after the time of his relationship with the mother of his child. For example, he had a romance with Florence Ballard (that was actually portrayed in the film, but by this time, Josephine was much more "out of the picture" than the film depicts.) Also, there are scenes in the film that show Otis with Josephine during time periods that just aren't factually accurate - in real life, Otis was in his second marriage during a time-period in which he is shown with Josephine in the film.
During the scene at The Rock and Roll Hall Of Fame Induction ceremony in 1989, the actor playing Glenn Leonard was seated at the table with the current lineup of The Temptations, at that time. By then, however, Ron Tyson filled the role of first tenor/falsetto vocalist in the group and not Glenn Leonard. Tyson replaced Glenn Leonard in 1983.
In the movie, Otis is shown in Al Bryant's milk truck "making out" with his girlfriend Josephine, when, over the radio - the DJ summons Otis's group "Otis Williams and the Distants" to the studio. However, according to Otis Williams himself, in his autobiography "The Temptations" - Otis was doing a much more mundane activity when he heard the DJ summon his singing group over the radio airwaves. Otis was actually washing dishes - not making out with his girlfriend.