Factual error: When Steve Martin dies with the mask on, the inflation bulbs (the little black bags that inflate and deflate) deflate completely. Actually they should INFLATE completely and stay that way. The gas is still on full blast and Steve is no longer inhaling (which would cause them to deflate). It was done only to emphasize Steve Martin's demise but it's factually incorrect.
Character mistake: Both in the movie (and stage) versions, Mushnik makes a verbal mistake. Seymour shows Mushnik his new plant (Audrey II) for the very first time, but seconds later when the plant suddenly droops, Mushnik asks Seymour, "Why is it always wilting like that?" Always? He's just seen the plant! The line should be, "Why is it wilting like that?" Some smart stage directors of the play version have wised up and changed the line.