It features extensive location filming in New Orleans and Florence, but a few key scenes were filmed in Southern California. The upstairs bedroom scenes at the Courtland mansion were shot at a house in Pasadena, since the owners of the New Orleans mansion used for the other shots were skittish about the crew being in the house. The car chase on the bridge was done in Long Beach, and the airport scenes were shot at LAX.
De Palma wasn't allowed to film inside the San Miniato al Monte church in Florence, because the Catholic Church in Italy banned all filming inside churches after an incident where a porno film was shot in a church after the crew lied to the clergy about their plans. Eventually De Palma found a small town that welcomed him to shoot the interior scenes inside their church.
Dawson Casting/Underage Casting: In the present day scenes, Sandra is 25, while Geneviève Bujold was 33. Michael and Lasalle are supposed to be in their 40s. Cliff Robertson was 52, but on the other end of the spectrum, John Lithgow was just 30.
Dueling Works: In a "Hitchcock Homage vs Actual Hitchcock" duel with Family Plot, which was released a few months before Obsession, and a "De Palma vs De Palma" duel with Carrie, released a couple months later.
He Also Did: It was Bernard Herrmann's idea to have the opening credits sequence be a montage of photo slides of Michael and Elizabeth and shots of the Florence church.
Hostility on the Set: De Palma and Cliff Robertson reportedly didn't get along, and De Palma later accused Robertson of sabotaging the film (via a lackluster performance) because Bujold was very obviously out-acting him.
I Knew It!: Reviewers at the time noted that the plot twist is pretty easy to figure out.
Unlike Lithgow, Cliff Robertson doesn't attempt a Southern accent.
Geneviève Bujold uses her natural French Canadian voice for Sandra, but it's passable as an Italian accent, especially when she trills her Rs. To avert any What the Hell Is That Accent? issues, she doesn't speak in her scenes as Elizabeth.
Much of Paul Schrader's original story outline got dropped for the final shooting script. Most prominent was a Distant Finale ending: rather than be reunited at the airport in 1975, Michael gets institutionalized following the killing of Lasalle, while Sandra is harbored by nuns at the church in Florence following her suicide attempt on the plane. When he's released in 1985, he flies to Florence with an actual Briefcase Full of Money, and finds Sandra in the church, then it ends basically the same way the final film does. Another idea was to have the actor playing Michael's psychiatrist also play a kidnapper and a romantic suitor of Sandra's in Italy.