Time span
I've watched this film a couple times again recently, and I've been wondering what the duration of time the movie covers is.
When we first see Alex, her assistant mentions that she had to go back a year to find someone else who had died of Ondine's curse. That of course is Sam Peterson, the publisher who was Catherine/Rennie's first victim (that we know of, anyway). So that means after Catherine (or Rennie, or, as they used to see the old action shows in the 70's, whatever her real name is) is shown arriving home in NYC, the movie skips about a year to where we meet Alex.
You have to figure, therefore, there's at least a year between each husband. So I'm thinking there's gotta be a span of at least 3 years covered, possibly more. I'm thinking Catherine would probably "disappear" for at least a few months, to wait for the investigation of each husband's death to cool down, then she moves in on her next target. I'm thinking it's gotta take 9-12 months to get into each man's life to the point they're ready to not only marry her, but sign over their entire estate to her.