James Belushi was hired and fired as an extra on this film. If you look closely at the tracking shots of Amy Irving in her swimsuit, you can see Belushi in a pair of dark trunks a few steps behind Irving.
The amusement park scenes were filmed inside Old Chicago, the world's first indoor theme park and shopping mall. Built in 1975, closed in 1980, and finally razed in 1986, it was located in Bolingbrook, a southwest suburb of Chicago, IL.
For her role as a psychic with telepathic powers, Amy Irving attended a biofeedback clinic to learn about different levels of consciousness. After personally experiencing psychic changes, she had a better sense of how her character could transmit and receive messages.
A big star like Kirk Douglas was cast as the lead in this film because director 'Brian de Palma' had felt that his previous picture Carrie (1976) had suffered at the box-office without a name draw-card.
Publicity for this film stated that this was the comeback movie for actress Carrie Snodgress who had not appeared in a theatrical film for eight years (since 1970 when she appeared in both Rabbit, Run (1970) and Diary of a Mad Housewife (1970)), her last credit at the time having being seven years previous in the 1971 tele-movie The Impatient Heart (1971).
The trivia item below may give away important plot points.
The special effects scene showing John Cassavetes exploding had the actor in the shot bleeding and convulsing from which then a lamp falls to the ground creating a brief white flash. From this, in editing, the actor was replaced with a dummy, which was rigged to explode, the shot filmed from a number of different angles.