How do screenwriters get away with using coincidences in their stories?

Remember that time in THE DARK KNIGHT RETURNS when Bruce suddenly - magically - returned to Gotham, and you were like "WTF?!"  Well, it turns out that many of the best films have moments that are just as coincidental or contrived (or a flock of Giant Eagles) and yet get away with it. Does Pixar's "rule" that it is 'cheating to use coincidences to get your characters out of trouble', always apply?

In exploring how to get the audience to buy into these moments where the writer needs story to intrude over character or even logic, Stu and Chas dive into FINDING NEMO, MICHAEL CLAYTON and PULP FICTION (as well as honourably mentioning THOR II, OUT OF SIGHT, MAD MAX FURY ROAD, EMPIRE STRIKES BACK, INDEPENDENCE DAY and those bloody Giant Eagles in both RETURN OF THE KING and THE HOBBIT).

In back matter, we talk about moving forward vs working backwards when developing screenwriting skills.

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