An unscripted
mistake in Back to the Future led to significant elements in the sequels.
When Marty McFly is about to be shot by the Libyans at the Mall, behind him on the hill overlooking the parking lot a figure appears. This figure seems to be the Marty McFly, from an hour later in the film, returned from the future too late to save his friend Doc.
When Robert Zemeckis was asked if this shadowy appearance was on purpose, he denied it, and claimed that it was a fortuitous error. He used more multiple appearances in the later BTTF films.
Another film error that added to the mystique of the film is the ghost in Three Men and a Baby.