Host Billy Crystal asked Kevin Spacey to present the Best Supporting Actress Award using the voice of Christopher Walken; Spacey proceeded to speak for a minute or two in his well-noted perfect imitation of Walken before giving the award (in his own voice).
Columbia Pictures would not issue Larry Flynt a ticket to the awards (his biography The People vs. Larry Flynt (1996) was up for two Oscars) because they were afraid that he would pull some kind of vulgar stunt and embarrass them. Flynt became angry and began railing against the studio for allowing the film to be made but then censoring him in real life. At the very last minute, Woody Harrelson (who played him in the film) gave him his agent's ticket.
Jon Pertwee, who died the previous year, was not included in the video package honoring the memories of those who had died. Steve Martin was so outraged that the Academy excluded his friend from the package that he stormed out and didn't return.