The phrase "cautionary about" is correct and commonly used in written English.
It is typically used to indicate that someone is being cautious or warning about something. Example: "The government released a statement cautionary about the dangers of excessive sugar consumption."
I do agree that there's something (even several things) cautionary about the movie, but not that.
In the end what is compelling and cautionary about Ms. Holloway's story is not simply that something terrible happened but that she was too wedded to the idea of her daughter's straight-A exceptionalism.
If there's anything additionally cautionary about "Cold Weather," it's in the suggestion that the technically crude do-it-yourself qualities that are a commonplace of microbudget filmmaking should no more be fetishized than the so-called production values of Hollywood productions.
However, the authors are cautionary about the validity of this comparison, because of potential differences between those who were and were not placed.
The story themes are often cautionary about too-powerful central authority and its capacity to do bad while being considered by the majority as good.
Like other dystopian works of art, it is derivative and reflective of our current moment, and cautionary about the path we are headed on.
The movie is self-consciously anti-war, full of enough cautionaries about greed and profiteering from international conflict to stand as a moral tale.
Stories about great men and women, or cautionary tales about individual failures, were meant to instill Roman values (mores maiorum).
We like cautionary tales about the dangers of greed and reassuring distinctions about the sources and uses of wealth.
Nominally a story about sex, lies and faithfulness, "Last Night" is more truly a cautionary tale about mousetrap narratives.
