As Andrew Strong is about to go into the main Chorus towards the end of "Try A Little Tenderness", when the drums kick in, the piano player goes for a strike down the keys, but in the next shot he's playing it normally.
When some members of the group are talking about some famous Rock Stars have died, "Outspan" mentions Cass Elliot cause of death as a heart attack. The others correct him by saying it was by choking on her own vomit but it was indeed due to a heart attack.
When Jimmy's dad tells him that Elvis is God, Jimmy said he never pictured God with a fat gut singing "My Way" at Caesar's Palace. Elvis actually performed at The Frontier and Las Vegas Hilton, but never Caesar's Palace.
Several band members are kicking a can in an alley waiting for the others just before the Mr. Chippy van scene. Joey's scooter appears around the corner in the distance at the end of the alley, approaching the group, and gets partway down the alley. We change camera angles, but this time there's someone walking a dog across the end of the alley where the scooter just entered, and the scooter continues toward us down the alley. We change camera angles again, and although the scooter is further down the alley, the dog walker is just starting to cross at the alley entrance again.
In the song I Never Loved a Man, Natalie sings lead. There's a lock of hair sticking out next to her right eye, very obvious in the closeups early in the song. Yet in the wide shots, and the closing closeup shot, her hair is perfectly under control. [Although not specifically addressed, this is explained in the directors commentary on the bonus DVD -- for the live shots, they only had two cameras, and recorded the closeups first, the wide shots later. Typically a single live song would be done dozens of times, taking most of a day.]
When we first see the band take off in the Mr. Chippy van, we see them go around a corner and off into the distance. The sign on the building at the corner is Bo Dollerns pub. Next, we have the flatulence scene in the van, then we're on the sidewalk as the van stops and the window is thrown open. What building do you see over the shoulder of "rock salmon" man? You guessed it -- Bo Dollern's pub -- guess the band's driving in circles.
When "The Commitments" play in their last gig, there is a big brass accompaniment. They are supposed just two. It's best heard during "In the Midnight Hour": there's a tenor saxophone from nowhere playing.