I am not fond of the hackneyed phrase to make a long story short (or its many trite cousins, including to cut to the chase and to get down to business). But it does not bother me all that much if used sparingly. What does grate on me is the truncated, slangy version long story short, as in these annoying examples:
From Time — Long story short, he quit his job to become a musician.
From The Atlantic — Long story short: our system of finance is irrational and disorganized and presents perverse incentives to doctors, hospitals, and communities.
Perhaps I’m being overly rigid: the shorthand version of the phrase, after years of irritating repetition, may have become idiomatically acceptable (like the even more irritating push the envelope). It certainly has the advantage of brevity. But I cannot help thinking less of writers who compound their banality with slovenliness.
My advice: avoid the phrase entirely, but, if you cannot help yourself, at least use the standard idiomatic expression and stay away from its bastard offspring.