Which element of a short story is most important for a mystery story?

First and foremost the detective story must have somebody who detects. Deduces things from collecting clues.

After this there is considerable variation:

* The who dun it - finding the person who did the deed

* They why dun it - discerning the motive

* The how dun it - the locked room murder

* police procedural - leg work

* court challenge - proving that what was done was actually a crime worthy of punishment