The film's initial cut received an NC-17 rating, the second cut was R-rated. However, the studio decided to go for a PG-13 rating, which required drastic cutting of multiple scenes, and was done against the wishes of director George Armitage. Armitage quit the project during the editing stage, and has never seen the theatrical cut.
The finished PG-13 rated film appears to have a great deal of censoring, from what was originally cut as an R-rated film. As such, several "f" words are overdubbed with much less strong words (with their mouths visibly saying something else). Also, it appears the romance between Jack and Nancy had been toned down slightly, by removing scenes and moments that appear in the film's theatrical trailer.
Several bits from the trailer do not appear in the finished film. These include Nancy pulling a gun on Jack (and the resulting dialogue of her asking, "What kind of girl do you think I am?" with Jack replying, "The kind of girl who had a gun on me thirty seconds ago," and Nancy saying "Yeah, but I didn't SHOOT you..."); Nancy and Jack actually getting into the car as they steal it (she playfully says, "Let's make out!" and Jack replies, "Eaaasy..."); a couple shots of Jack and Nancy kissing; Jack and Nancy on a skateboard; and finally Jack making a playful growling sound.