After a run of successes at the box office, John Landis stumbled with this thriller. No doubt at the time people blamed The Twilight Zone accident or its then-relatively-unknown stars (Jeff Goldblum, Michelle Pfeiffer) - but I think the problems were more in the script and tone.
Landis seems to be going for a Hitchcock type thriller full of off beat touches - there's a Macguffin (diamonds from the Shah of Iran), various assassins after the lead couple (some Iranians including Landis himself, plus some black dudes working for a Frenchman, David Bowie), matriarchs (Vera Miles, Irene Papas), dodgy rich people, a mysterious blonde, an innocent man who gets caught up in mayhem. And there's no reason a modern day Hitchcock couldn't work - look at Silver Streak and Foul Play.
But Hitchcock (and his successful imitators) always made sure his heroes were front and center - they were driving the action, had big stakes (normally by being falsely accused of some crime). Goldblum here is basically a passenger - the real hero is Pfeiffer, Goldblum just goes along for the ride. It's like telling The 39 Steps from Madeleine Carroll's viewpoint - only you couldn't really cut Carroll out of that movie but you could cut Goldblum out of this which isn't a good idea when he's the star. The balance of the movie is thrown out because he still gets the bulk of screen time but he's kind of hanging around.
Tonally it doesn't quite work. Landis mixed tones successfully in An American Werewolf in London but less so here - he allows the Iranian assassins (in particular the one played by himself) to be too comic at times (a little but is amusing, but the guy is a killer and it reduces the threat); also the scene where the killers drown Kathryn Harrold, who is guilty of nothing more than being in the wrong place at the wrong time, just felt mean.
This sounds like I didn't like the movie, but actually I did. You never quite know what's going to happen; Goldblum is likeable and Pfeiffer a perfect Hitchcockian blonde; I enjoyed all the director cameos (Roger Vadim makes a fine villain); there are some excellent support performances from people like Richard Farnsworth, and David Bowie (Vera Miles admittedly goes over the top); some scenes are classic, such as Goldblum discovering dead bodies while Abbott and Costello Meet Frankenstein plays on TV (Landis makes sure Bud, Lou, Bela and Lon are all credited!) It's a true original. I just wish it had aped its Hitchcock models better.