I think it was in a workshop of Bill Martell's that I first heard that you get ONE coincidence per story, and I've stuck to that rule. I think it's a good policy to follow.

Thanks, Scott. That makes a lot of sense. I guess it's yet another aspect of screenwriting that just takes some trial and error to figure out.

I forgot where I read it, but someone said, the audience will accept a coincidence early in the story, as part of setting up the world of the story - after all, things do "just happen" in real life - but not later in the working out of the story. The working out has to reflect story/situation logic. This dovetails exactly with your coincidence/conceit distinction.

This helped me understand why Dennis Lehane's stories don't quite work for me, at least in the movies made from his books (MYSTIC RIVER, GONE BABY GONE, and SHUTTER ISLAND) - there are too many coincidences, they come late in the story, and are attempts to cover the flaws in the logic of the story.

This is really helpful. Thanks!

In action movies, give the villain coincidences, especially in the third act -- "Out of the frying pan into the fire"

Sorry, but I don't buy your coincidence vs conceit taxonomy.
IMO, a more useful question is, why do some coincidences work (in the story) and some don't. What's the MTC (Maximum Threshold of Coincidence) that audiences will accept? Most films, even great films, have coincidences but, for whatever reason, we buy into them. In Casablanca, Rick acquires the letters of transit on the exact night that Ilse walks into the bar needing them. In Shawshank Redemption, Tommy, one of only three people in the world who knows Andy is innocent, ends up in the same prison and group as Andy. Anyone want a refund?