Deliberate mistake: When the nuns sing for the first time in the church in perfect tone then break into the dance version of the song, the reverend mother acts like it's the first time she has heard it. In reality, she would have heard the rehearsals as the convent is very quiet and you can hear the choir rehearsing when she tells Deloris she will join the choir.
Suggested correction: She may have heard it, but never seen it. What startled her were the moves.
Deliberate mistake: When Wayne begins playing the "Excalibur" guitar, the clerk stops him and directs him to a "No Stairway to Heaven" sign. The problem is that the guitar riff Wayne started playing sounded nothing like "Stairway to Heaven" so the clerk had no reason to interrupt him. Evidently the intro to "Stairway" was actually played in the theatrical version of the film, but its exclusion in the home video release makes the scene rather dubious.