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.
Character mistake: At the very beginning of the movie, young Delores' teacher tells her to go to the board and right down the names of the apostles alphabetically. Delores writes down, John, Paul and Peter with the nun nodding in approval until Delores writes down Elvis. Paul wasn't one of the original apostles and since the nun told Delores to write it down alphabetically, the first name on the board should have been Andrew but, the nun doesn't stop and correct Delores after she writes John's name down first.
Factual error: At the end of the movie when they put on the concert for the Pope, Dolores is no longer wearing a full habit as her hair and ears (with big hoop earrings are visible). She isn't wearing a full habit because she would not have been allowed to, especially in the Pope's presence, since it was made public that she's not really a nun. However, during the end credits there is a picture of her with the Pope, and she is wearing a full habit.