In the scene where Captain Picard and the Admiral are in Picard's ready room, there is a cloth on the back of Picard's chair. This is the cloth given to him by the Mintakans in Who Watches the Watchers (1989), an episode in which Starfleet used a duck blind for anthropological purposes.
Captain Picard was originally going to kill Data in this film, a decision fully supported by Brent Spiner, who felt he was getting too old to play the character. This was vetoed by Sir Patrick Stewart. Spiner's script came with a note reading, "Better luck next time".
When Data is malfunctioning, Captain Picard gets him to recite W.S. Gilbert and Arthur Sullivan's "H.M.S. Pinafore". In the Isaac Asimov story "Runaround", a malfunctioning robot recites Gilbert and Sullivan while evading capture by his human masters. Much of Data's character is taken from Isaac Asimov's writings (such as Data's "Positronic Net", adapted from Asimov's "Positronic" brains).
The first Star Trek film in which all of the space shots were computer-generated.
According to a leaked manuscript, "Fade In: The Writing of Star Trek: Insurrection" (written by Michael Piller years before his death, and never released because of studio concerns about the content of said manuscript), initial concepts for this film were far removed from the final product. The first treatment (called "Star Trek: Stardust") involved Picard and a fellow cadet named Hugh Duffy (who were friends at Starfleet Academy) meeting up after almost three decades because of different circumstances. Duffy has become a renegade who has tried to provoke a war between the Federation and the Romulan Empire, and Picard must travel to the Neutral Zone to bring him back. Picard eventually finds Duffy and risks his career to help the other officer thwart a plan by the Romulans to take over a planet housing "the fountain of youth". At the end, Picard gets arrested (and stripped of his rank) by Starfleet due to his actions during this film. The plot was similar to Heart of Darkness, and featured numerous references to various episodes of Star Trek: The Next Generation (1987).