Deliberate mistake: In the torture scene, Mr Blonde turns the radio on and listens to "Stuck in the Middle with You" as he proceeds to torture the cop. Mr Orange shoots him before Mr Blonde turns the radio off, but somehow the radio is never heard again in the film.
Deliberate mistake: When the penguin goes into the cemetery, he bumps a tombstone and it moves. Almost certainly a tribute to legendarily poor director Ed Wood, who Tim Burton later directed a biopic of - this exact thing happened in one of his films. (00:39:15)
Deliberate mistake: The extras used in the scene when Danny gets assigned the case appear again as members of the jury. If Danny's colleagues were called as jury members for a trial all would have to declare a conflict of interest and be ineligible to hear the case. (00:09:30 - 01:03:25)
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.