These aren't cast recordings, but two of the most noticeable (and funniest0 mistakes in the music industry are:
"I Saw Her Again Last Night" by the Mamas and the Papas.
During the climatic moment, one of the guys came in with "I Saw Her" too early.
"Baby, You Got What It Takes" by Dinah Washington and Brooke Benton.
Dinah and Brooke were supposed to record an album together with six duets.
During the second verse of "Baby, you got what it takes", Brooke starts singing, and Dinah says "You're back in my spot again, honey!" He stops, so she sings her verse. "I Like you're spot", he says. When her verse is finished she says "Now it's you!" This is obviously upsetting to her. When the recording was finished a huge fight ensued. They recorded a second song "A Rockin' Good Way", and in the end they began ad-libbing. Dinah would say things like "Just stay outta my spot" - all tongue in cheek.
He got angry, and even angrier that the producers kept it in the recording. They only recorded four songs together, as Dinah and Brooke never got along. The project was never completed, and the album only released four of the duets, while the rest of the numbers were solos.
"Do you know what pledge time is, Andrew"? said the PBS Executive.
"Yes", Lloyd Webber replied. "My 50th birthday special must be one program that gets done a lot."
"No", mused the man from PBS heedlessy. "Not so much. Our Stephen Sondheim Carnegie Hall concert. That's a big one."
Spoons, forks and knives seemed suddenly to suspend their motion in horror, all around the table.