Its flaws
It's an enjoyable film, by all means (even watching it more than once), mostly because of the performances.
****SPOILERS AHEAD*****
But I do find it rather puzzling that they chose the murderer to be a person completely uninvolved in the plot - a person who was in fact *unseen* by the viewer until the actual unraveling of the mystery. That's such a huge beginners' mistake, an absolute "no-no" - in film as well as in writing!
Also, I LOVE Cyd Charisse, but her physical type is *identical* to Ava Gardner's. What were they thinking? Didn't they know that you're not supposed to confuse the spectator by introducing visually similar people (unless it's part of the plot, obviously)? Or was that supposed to be some kind of a blurry, veiled "statement"?
Besides, was her character necessary at all? I don't think so. Her (very slight) role could've been easily taken over by a minor character or even different characters etc.
It's baffling.
And it's also a pity because it could have been a much, much better picture.