Arnold Schwarzenegger had a near-fatal accident on set during the horse riding scene, when his horse got startled and ran out of control. Schwarzenegger managed to slide off the horse, but did this near a 30-foot drop-off. His personal stunt man saw what happened and was able to grab him before he went over the ledge.
When Harry tells Gib that Helen is having an affair, Gib tells a story about his second wife taking everything when she left him, even the ice cube trays from the freezer. This is a direct reference to Tom Arnold's divorce from Roseanne Barr that was happening at the same time - she was reported to have taken his ice cube trays when she left him as well. Arnold told the story to James Cameron on the set while saying: "What kind of sick bitch takes the ice cube trays out of the freezer?" Cameron thought the line was hilarious, and incorporated it into the film.
Arnold Schwarzenegger's biggest challenge for the movie was not doing all the physical stunts, but dancing a tango. He had to take dancing lessons to realistically perform the dance. He rehearsed the scene for about six months as he wanted to make sure he was as good at the tango as Al Pacino was in Scent of a Woman - Profumo di donna (1992) (which used the exact same song, 'Por Una Cabeza').
The set of bra and matching panties worn by Helen Tasker during the striptease scene were Jamie Lee Curtis's own. Curtis rehearsed the scene extensively with director James Cameron, and it was there and then that the fall she makes in the middle of the dance was conceived (it didn't happen spontaneously during the rehearsal or the actual shooting, as is often claimed). Arnold Schwarzenegger was not told of this beforehand, and this is hinted at when Harry briefly sits up in alarm, realizes that he is breaking character, and then relaxes. They did another take with the same gag, but Harry's reaction didn't look as spontaneous.
Arnold Schwarzenegger wasn't supposed to drop the tape recorder. James Cameron liked it, and kept it in.
James Cameron: [White Frame] When Helen punches Harry in the face, a single solid white frame is spliced in at the moment of impact. This film trick accurately conveys the flash a person sees when they get hit in the head. It was also used in The Abyss (1989) when Cat punches Coffey in the face, and in Terminator 2 - Il giorno del giudizio (1991) when Sarah clocks Douglas in the face with the mop handle.